Quantum Optics V Book of abstracts

Cozumel, Mexico

Fiesta Americana Cozumel Dive Resort November 15-19, 2010

Supported by:

Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE)

Optical Society of America (OSA) Joint Quantum Institute (JQI)

Consejo Nacional de Ciencia y Tecnología (CONACYT) Academia Mexicana de Ciencias (AMC)

Universidad de Guanajuato (Campus León)

Local Committee

Héctor Moya-Cessa (INAOE)

Luis A. Orozco (University of Maryland)

Andrei Klimov (Universidad de

Guadalajara) Alfred U’Ren

(ICN – UNAM)

Scientific Committee

Octavio Castaños Rocío Jáuregui Peter L. Knight José Luis Lucio

Sascha Wallentowitz

Quantum State Engineering and the Simulation of Nature

Peter Knight

Blackett Laboratory, Imperial College, London SW7 2AZ, UK

A major growth area of quantum information science is the potential to realize Feynman’s early idea of simulating quantum processes. With a given quantum resource- an array of qubits that can be manipulated with external couplings, one can simulate efficiently quantum processes which occur naturally but which cannot easily be simulated by classical methods given the size of the state space involved.

Many potential realizations have been proposed using trapped laser cooled ions or cold atoms in optical lattices, with goals for example of understanding the ground state of high temperature superconductors through the simulation of the Bose-Hubbard Hamiltonian. I will discuss how quantum Hamiltonians and indeed dissipative couplings can be engineered to meet these goals. Such an approach has considerable merits but needs to be used with some caution to ensure what is simulated has a real-world counterpart. As an example, I will discuss the recent experiment of the Esslinger group [1] on the observation of the Dicke quantum phase transition with a superfluid gas in an optical cavity. On the one hand this is a beautiful and convincing experiment, but raises fundamental questions about the nature of quantum simulations. I will review the origins of the Dicke quantum phase transition [2] which derives from an approximate and non-gauge invariant treatment of many atoms interacting via electric dipole transitions by Hepp and Lieb. A more precise treatment of the many atom- radiation coupling by Bialynicki-Birula and Rzazewski [3] proved a “No-Go” theorem, showing that the Dicke superradiant phase transition cannot occur in a general system of atoms or molecules if only charges (not intrinsic magnetic moments) of the particles interact with a finite number of radiation modes in the dipole approximation. So what has been simulated: a Hamiltonian that theorists have invented which does not normally occur, or a real-life Hamiltonian? I will discuss what lessons we might learn from this example, and look at other examples of Nature exploiting quantum coherence (or not). [1] K Baumann et al, Nature 464, 1301 (29th April 2010) [2] K Hepp and E Lieb, Ann Phys 76, 360 (1973) [3] I Bialynicki-Birula and K Rzazewski, Phys Rev A19, 301 (1979)

Coherence, Entanglement and Quantum Discord in atomic systems.

M.Orszag, Maria de los Angeles Gallego We study the behavior of two qubits in various types of reservoir, with particular emphasis on the relation between the Decoherence Free Subspace, entanglement, quantum discord and classical correlation, in the cases of sudden death, revival and generation of entanglement.

Beyond the Rayleigh limit in optical lithography

M. Suhail Zubairy

Institute of Quantum Studies and Department of Physics and Astronomy,

Texas A&M University, College Station, Texas 77843-4242 zubairy@tamu.edu

It is well known that the classical schemes for microscopy and lithography are restricted by the diffraction limit. The precision with which a pattern could be etched in interference lithography is limited by the wavelength of the light. In recent years, a number of schemes have been proposed via quantum interferometry to improve the resolution. Some of these schemes are based on quantum entanglement and multiphoton processes.

In this talk we shall discuss several schemes for ’quantum’ lithography using classical light. In the first scheme [1, 2], we consider a particular multiphoton absorbing substrate. This scheme has the same effect as using an entangled light beam but the advantage of using classical light is that the multiphoton absorption are more efficient and thus afford a practical scheme. Another advantage is that the generalization to one and two dimensional patterns is possible.

In the second scheme [3], we relax the condition of multiphoton processes. In this scheme, we describe a novel approach for the generation of subwavelength structures in interferometric optical lithography. Our scheme relies on the preparation of the system in a position dependent trapping state via phase shifted standing wave patterns. Since this process only comprises resonant atom-field interactions, a multiphoton absorption medium is not required.

In the third scheme [4], we propose a simple quantum optical method to do the sub-wavelength lithography. Our method is similar to the traditional lithography but adding a critical step before dissociating the chemical bound of the photoresist. The subwavelength pattern is achieved by inducing the multi-Rabi-oscillation between the two atomic levels. The proposed method does not require multiphoton absorption and the entanglement of photons. This method is expected to be realizable using current technology.

References 1. P. R. Hemmer, A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, Phys. Rev. Lett, 96,

163603 (2006). 2. Q. Sun, P. Hemmer, and M. S. Zubairy, Phys. Rev. A, 75, 065803 (2007). 3. M. Kiffner, J. Evers, and M. S. Zubairy, Phys. Rev. Lett, 100, 073602 (2008). 4. Z. Liao, M. Alamri, and M. S. Zubairy, (unpublished).

Quantum lithography—possibilities and limitations

G. Björk1, C. Kothe

1,2, M. Bourennane

2, and S. Inoue

3

1School of Information and Communication Technology,

Royal Institute of Technology (KTH), Electrum 229, SE-164 40 Kista, Sweden 2Department of Physics, Stockholm University, SE-109 61 Stockholm, Sweden

3Institute of Quantum Science, Nihon University,

1-8-14 Kanda-Surugadai, Chiyoda-ku, Tokyo 101-8308, Japan

Quantum interference lies at the heart of quantum mechanics, and is the basis for many

applications. In the last few years there have been many studies and experiments to delineate

to what extent quantum states can surpass classical state, in interferometers and in imaging

applications. The studies have not yet lead to a consensus: There are still differences in

opinions as to what extent, e.g., entanglement is needed as a resource to surpass the standard

classical limits and there is also an ongoing discussion about the efficiency of quantum

lithography.

On the basis of two recent experiments [1,2] I will discuss these issues and demonstrate that it

rather is multi-photon absorption (or a multiplication of one-photon absorption events) than

entanglement that lead to phase super-resolution. I will also argue that quantum lithography

seems to have a very unfortunate scaling behaviour with the respect of the exposure dose (or

exposure time) as the number of image pixels increase [3]. Effectively, this may pose an

effective obstacle for quantum lithography to become a practical alternative to ordinary

lithography.

[1] C. Kothe, G. Björk, and M. Bourennane, “Super-resolving phase

measurements without entanglement or joint detection”, Phys. Rev. A.

vol. 81, pp. 063836, 2010. arXiv 1004.3414

[2] W. H. Peeters, J. J. Renema, and M. P. van Exter, Phys. Rev. A 79, 043817 (2009).

[3] C. Kothe, G. Björk, M. Bourennane, and S. Inoue, “On the

feasibility of quantum lithorgraphy”, arXiv:1006.2250

Nonlinearity improves precision quantum metrology

Alfredo Luis Departamento de Óptica, Universidad Complutense, Madrid, Spain

Quantum metrology studies precise detection of weak signals. The signal is inferred by monitoring the change induced by a signal-dependent transformation on a probe state. The main objective is to obtain minimum uncertainty in the inferred value of the signal with fixed resources, usually represented by the number of particles (atoms or photons) in the probe state. Traditionally it has been assumed that the signal-dependent change is implemented by linear input-output processes. This is the case of standard interferometry and spectroscopy. Linear schemes lead to signal uncertainties scaling as 1/N, this is the inverse of the number of particles N in the probe state. To approach this limit the probe must be prepared in a strongly nonclassical state, typically squeezed or N00N states. Deterministic preparation of theses states typically requires propagation in nonlinear media. Recently it has been shown that precision can be greatly improved if the signal-dependent probe transformation is implemented by nonlinear input-output processes. More specifically, if the transformation is generated by a Hamiltonian proportional to the k’th power of the number operator then the signal uncertainty scales as the inverse of the k’th power of the total number of particles 1/Nk . Moreover, the improvement over the linear case holds even if the probe is prepared in a classical state. For classical probes, the signal uncertainty scales as the inverse of the (k-1/2)’th power of the total number of particles 1/Nk-1/2 . Even for the smaller nonlinearity, this is k=2, this gives uncertainty scaling as 1/N3/2 that is much below the linear-case uncertainty 1/N when N is very large, as it usually holds. A key advantage of this result emerges from the robustness of classical states under practical imperfections, so that under realistic conditions the scaling with the number of particles is preserved. The signal uncertainty can be readily formulated in terms of the quantum Fisher information. For classical detection (this is classical probes and linear transformations) the quantum Fisher information is linear in the number of particles. Therefore, to do better than classical requires a nonlinear dependence of quantum Fisher information on the number of particles. This can be achieved with nonclassical probes in linear schemes, or with nonlinear schemes, even if the probe is classical. Comparing these two alternatives we get that it is advantageous to use nonlinearity in the probe transformation rather than in the probe preparation. This is so concerning both the scaling of the signal uncertainty with the number of particles and the robustness under practical imperfections. It is shown that the nonlinear improvement does not arise because of nonclassicality or entanglement produced by the signal-induced transformation, but via signal amplification caused by the nonlinearity.

P Barberis-Blostein 1, D G Norris 2, L A Orozco 2 and H J Carmichael 2,3

1 Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510,

México, DF, México 2 Joint Quantum Institute, Department of Physics, University of

Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA

3 Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand

It was recently shown how to implement a quantum probabilistic error correction protocol [1] in a solid state qubit [2,3] and in a photonic qubit [4]. In this talk it is shown how one can implement a quantum probabilistic error correction protocol in an open quantum system consisting of a single atom, with ground- and excited-state Zeeman structure, in a driven two-mode optical cavity. The ground-state superposition is manipulated and controlled through conditional measurements and external fields, which shield the coherence and correct quantum errors. Modeling an experimentally realistic situation demonstrates the robustness of the proposal for realization in the laboratory. [1] Koashi M and Ueda M 1999 Reversing measurement and probabilistic quantum error correction Phys. Rev. Lett. 82 2598 [2] Korotkov A N and Jordan A N 2006 Undoing a weak quantum measurement of a solid-state qubit Phys. Rev. Lett. 97 166805 [3] Katz N et al 2008 Reversal of the weak measurement of a quantum state in a superconducting phase qubit Phys. Rev. Lett. 101 200401 [4] Kim Y-S, Cho Y-W, Ra Y-S and Kim Y-H 2009 Reversing the weak quantum measurement for a photonic qubit Opt. Express 17 1197885

Cloning of a Continuous-Variable Entangled StateAlberto M. Marino1, Raphael C. Pooser2, Vincent Boyer3, Kevin M. Jones4, and Paul D. Lett1

1Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland, Gaithersburg, Maryland 20899 USA2Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 USA

3MUARC, School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom4Department of Physics, Williams College, Williamstown, Massachusetts 01267 USA

email: alberto.marino@nist.gov

1. Introduction

A distinctive aspect of quantum mechanics is the inability to obtain a perfect copy of an arbitrary quantum state,a result know as the no-cloning theorem [1]. Nevertheless, it is still possible to implement a device that can obtainthe best possible copy of any quantum state. We show that we can implement such a device and use it to clone one ofthe beams from continuous variable (CV) entangled twin beams while preserving the entanglement between the twocopies of the cloned mode and the original unmodified mode [2].

2. Quantum Cloning of a CV Entangled State

The implementation of a quantum cloning device in the CV regime is composed of a phase-insensitive amplifierfollowed by a beam splitter [3]. We use four-wave mixing in a double-lambda configuration as the phase-insensitiveamplifier [4] in the cloning device to study the cloning operation on one of the modes of entangled twin beams. Afterthe amplifier a variable attenuator simulates one of the outputs of the beam splitter. By setting the gain-attenuationproduct to one, this configuration allows us to study a range of cloning configurations, including asymmetric clones(when clones have unequal intensities) and the usual case with an amplifier gain of 2 followed by a 50/50 beam splitterto generate two clones with intensities equal to the input state.

We characterize the operation of our cloning device by measuring the amount of entanglement left between oneof the clones and the unmodified beam of light after the cloning operation. For this purpose we use two differententanglement criteria. The first is given by the inseparability criterion [5]

I = 〈∆X2−〉+ 〈∆Y 2

+〉< 2, (1)

where 〈∆X2−〉 is the amplitude difference noise and 〈∆Y 2+〉 is the phase sum noise. According to this criterion, the

presence of squeezing in both the amplitude difference and the phase sum is a sufficient condition for CV entanglement.A stronger degree of quantum correlation is given by EPR entanglement, in which case it is possible to remotely inferthe properties of one system (to better than its standard quantum limit) through measurements on the other correlatedsystem. This type of entanglement can be quantified with the conditional variances of system a given system b, VXa|Xband VYa|Yb

. We can define the EPR parameter Eab = VXa|Xb·VYa|Yb

such that Eab < 1 indicates the presence of EPRentanglement [6]. In practice, the conditional variances are calculated from joint quadrature measurements.

With this method we have shown that CV entanglement (I < 2) is still present after applying the cloning operationto one of the modes of entangled twin beams over a range of operating parameters for the cloning device. In particular,we found that there is still a significant amount of entanglement after symmetrically cloning (two output copies of theinput state) one of the modes, such that the clones are entangled with the other unmodified mode from the originalstate. On the other hand, the EPR parameter reaches its limit of 1 with gain more quickly than the inseparability, suchthat symmetrical cloning while preserving EPR entanglement is not possible. This is due to the fact that the amountof EPR correlations in a system is dependent on the purity of the state while the inseparability is not.

3. References

[1] W.K. Wootters and W.H. Zurek, Nature 299, 802 (1982).[2] R.C Posser, A.M. Marino, V. Boyer, K.M. Jones, and P.D. Lett, Phys. Rev. Lett., 103, 010501 (2009).[3] S.L. Braunstein, N.J. Cerf, S. Iblisdir, P. van Loock, and S. Massar, Phys. Rev. Lett., 86, 4938 (2001).[4] C.F. McCormick, A.M. Marino, V. Boyer, and P.D. Lett, Phys. Rev. A 78, 043816 (2008).[5] L.M. Duan, G. Giedke, J.I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).[6] M.D. Reid, Phys. Rev. A 40, 913 (1989).

Modeling nonlinear coherent states in photonic lattices R. de J. León Montiel and H. Moya-Cessa

INAOE

We show how nonlinear coherent states may be modeled in photonic lattices(waveguide array). A classical system is studied by using quantum-mechanical tools, we solve the wave guide array by introducing Susskind-Glogower phase operators, and by application to the “vacuum” (first site excited) we show that “nonlinear coherent states” are produced.

Capacities of cloning channels, optical amplifiers and beyond

Kamil Bradler∗

School of Computer Science, McGill UniversityMontreal, Quebec, Canada

The classical or quantum channel capacity is in general extremely hard to calculate. It is evenmore difficult to find an example of a quantum channel for which both capacities are known. Thereare only very few non-trivial examples and one of them is the dephasing channel [1]. We introducea whole new class of these rare gems – qudit cloning channels. The qudit cloning channel is anincarnation of the universal 1 → N qudit cloning machine. It has been clear for some time that thereis a close relation between cloning channels and optical amplifiers which have been widely studied fortheir role in quantum and classical communication (for some recent experimental proposals see, forinstance, [2]). Using this intimate connection we also obtained capacity formulas for linear opticalamplifiers generalizing some of the previously known results.

The whole story is revolving around the physical origin of, perhaps surprising, connection betweencloning channels, optical amplifiers and the Unruh effect which ultimately leads to the announcedcapacity proofs [3, 4]. The Unruh effect describes how inertial and non-inertial (uniformly accelerated)observers are not able to agree on the notion of a particle. This effect is the most dramaticallydemonstrated when the non-inertial observer accelerating through Minkowski vacuum feels a thermalbath while the inertial observer detects no particles at all. The Unruh effect defines a completelypositive map we call the qudit Unruh channel [3, 4]. The qudit Unruh channel has several interestingproperties. First of all, it can be written as an infinite-dimensional direct sum of 1 → N qudit cloningchannels. Furthermore, we observe that the Unruh channel and its cloning constituents satisfy aproperty called conjugate degradability [5, 4]. Channels are called conjugate degradable by virtue ofexistence of a conjugate degrading map transforming the output of the channel to its complementaryoutput up to complex conjugation. This paves the way to the proof of additivity of the quantumcapacity of the whole class of cloning channels including the Unruh channel itself. Finally, we observethat the complementary channels of all 1 → N cloning channels are entanglement-breaking [9, 7, 8].This is a key property for the proof of additivity of the classical capacity of the studied class ofchannels (again including the Unruh channel).

References

[1] I. Devetak and P. W. Shor, Communications in Mathematical Physics 256, 287 (2005).

[2] V. Josse, M. Sabuncu, N. J. Cerf, G. Leuchs and U. L. Andersen, Physical Review Letters 96,163602 (2006).

[3] K. Bradler, P. Hayden and P. Panangaden, Journal of High Energy Physics 08(074) (2009).

[4] K. Bradler, P. Hayden and P. Panangaden, arXiv:quant-ph/1007.0997.

[5] K. Bradler, N. Dutil, P. Hayden and A. Muhammad, Journal of Mathematical Physics 51, 072201(2010).

[6] K. Bradler, arXiv:quant-ph/0903.1638.

[7] T. J. O’Connor, K. Bradler and M. Wilde, in preparation.

[8] K. Bradler, D. Touchette, P. Hayden and M. Wilde, Physical Review A 81, 062312 (2010).

[9] P. W. Shor, Journal of Mathematical Physics 43, 4334 (2002).

∗kbradler@cs.mcgill.ca

Quantum nonequilibrium steady states: an exact solution

Marko Znidaric

Faculty of Mathematics and PhysicsUniversity of Ljubljana, Slovenia, and

Instituto de Ciencias FısicasUNAM, Cuernavaca, Mexico

Understanding quantum transport from microscopic equations of motions isone of the unsolved problems of theoretical physics. For instance, it is notknown what are the necessary requirements to observe diffusive transport.Close to equilibrium, where linear response theory is expected to be valid,one can study transport by calculating an equilibrium correlation function.To access a true nonequilibrium situation though one must either couplea system to a very large (an infinite) reservoir or take the coupling withbaths into account in an effective way, for instance by means of a masterequation. Analytic results are clearly preferred, unfortunately however allknown solvable systems display ballistic transport.I shall present an analytical solution for a one dimensional spin chain undernonequilibrium driving described by the Lindblad master equation. Exact ex-pressions for one and two-point correlation functions indicate diffusive trans-port. This is a first example of an exactly solvable diffusive quantum model.In the nonequilibrium steady state long-range correlations are present. Wealso identify a nonequilibrium phase transition between diffusive and ballistictransport regimes. In a special case, corresponding to a ballistic XX chainwith boundary driving, an exact solution is expressed in terms of matrixproduct ansatz with matrices if fixed dimension 4. The solution shows somesimilarity with classical exclusion processes.

References

[1] M. Znidaric, “Exact solution for a diffusive nonequilibrium steady stateof an open quantum chain”, J. Stat. Mech., L05002 (2010).[2] M. Znidaric, “A matrix product solution for a nonequilibrium steady stateof an XX chain”, arXiv:1006.5368.[3] R. A. Blythe and M. R. Evans, “Nonequilibrium steady states of matrix-product form: a solver’s guide”, J. Phys. A, 40 R333 (2007).

An Entropic Einstein-Podolsky-Rosen Steering Criterion

S. P. Walborn,1 A. Salles,1 R. M. Gomes,1 F. Toscano,1 and P. H. Souto Ribeiro1

1Instituto de Fısica, Universidade Federal do Rio de Janeiro,Caixa Postal 68528, Rio de Janeiro, RJ 21941-972, Brazil

We propose an EPR inequality based on an entropic uncertainty relation for complementary continuous variableobservables. This inequality is more sensitive than the previously established EPR inequality based on inferredvariances, and opens up the possibility of EPR tests of quantum nonlocality in a wider variety of quantum states. Weexperimentally test the inequality using spatially entangled photons. For a particular quantum state, our experimentalresults show a violation of the entropic EPR inequality, while the variance EPR inequality is not violated. We showtheoretically that our inequality identifies the non-local steering phenomenon, and is directly connected to securitybounds in quantum cryptography.

In 1935, Einstein, Podolsky and Rosen published the famous “EPR” paper, in which they concluded that quantumtheory must be incomplete, since it is in conflict with either realism or locality [1]. In the continuous variable regime,it has been shown by Reid that one can identify an “EPR paradox” when the inequality ∆2

min(XA)∆2min(PA) ≥ 1/4,

is violated [2]. Here ∆2min(XA) is the minimum variance in inferring property XA of system A given measurement of

property XB on system B. Moreover, it has been recently shown that the Reid-EPR inequality identifies steering, adistinct classification of quantum non-locality for states whose quantum correlation strength lies between entanglementand Bell non-locality [3, 4]. This shows that there exists a hierarchy of quantum correlations that has only been sparselyexplored.

Recently, we derived an entropic EPR-steering criterion [5]:

h(XA|XB) + h(PA|PB) ≥ lnπe, (1)

where h(XA|XB) is the conditional Shannon entropy. Violation of inequality (1) indicates a physical situation forwhich local realism is inconsistent with the completeness of quantum mechanics. The entropic inequality (1) is ingeneral more sensitive than the variance inequality. As an example, we consider a bipartite quantum system describedby the wave function

φ(xA, xB) = CnHn

(xA + xB√

2σ+

)e− (xA+xB)2

4σ2+ e

− (xA−xB)2

4σ2− , (2)

where Hn is the nth-order Hermite polynomial and Cn a normalization constant. Numerical analysis (n ≤ 15) showsthat the variance criteria identifies entanglement only when the ratio σ±/σ∓ ∼> 1+1.5

√n, while the entropic criterion

always identifies an EPR paradox, except in the case when the state is indeed separable (n = 0 and σ+ = σ−).To illustrate the utility of the entropic criterion (1), we experimentally tested it for a pair of spatially entan-

gled photons. A number of steps were taken to engineer the two-photon state, so that it was similar to that ofEq. (2) with n = 1. We tested the variance-product EPR inequality: ∆2

min(XA)∆2min(PA) = 0.44 ± 0.01 > 1/4

and∆2min(XB)∆2

min(PB) = 0.51± 0.01 > 1/4. Thus, the variance inequality is satisfied, and we cannot identify EPRnon-locality nor steering. Next we tested the entropic EPR inequality (1): h(XA|XB) + h(PA|PB) = 1.94± 0.04 andh(XB |XA) + h(PB |PA) = 1.99 ± 0.04. Both of these equations are less than lnπe ≈ 2.145 by more than 3 standarddeviations, indicating violation of inequality (1). Thus, the EPR non-locality and steering, which in this case is notidentified under the variance criterion, is revealed through test of the entropic EPR criterion (1).

Our inequality is also relevant to quantum cryptography with entangled continuous variable states using a two-basis(X and P ) protocol. For finite-sized coherent attacks, the lower bound for the secret key rate, corresponding to anupperbound of an eavesdropper’s information, is given by [6] ∆I ≥ lnπe − h(XB |XA) − h(PB |PA). It thus followsdirectly that the entropic EPR criterion (1) must be violated to guarantee a non-zero key rate (∆I > 0).

[1] A. Einstein, D. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).[2] M. D. Reid, Phys. Rev. A 40, 913 (1989).[3] H. M. Wiseman, S. J. Jones, and A. C. Doherty, Phys. Rev. Lett. 98, 140402 (2007).[4] E. G. Cavalcanti, S. J. Jones, H. M. Wiseman, and M. D. Reid, Phys. Rev. A 80, 032112 (2009).[5] S. P. Walborn, A. Salles, R. M. Gomes, F. Toscano, and P. H. Souto Ribeiro (2009), arXiv:0909.0147.[6] F. Grosshans and N. J. Cerf, Phys. Rev. Lett. 92, 047905 (2004).

Driving quantized vortices with quantum vacuum fluctuations

Francois Impens†, Ana M. Contreras-Reyes, and Paulo A. Maia NetoInstituto de Fisica, UFRJ, CP 68528, Rio de Janeiro, RJ, 21941-972, Brazil

Diego A.R. DalvitTheoretical Division, MS B213, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

Romain Guerout, Astrid Lambrecht, and Serge ReynaudLaboratoire Kastler Brossel, case 74, CNRS, ENS,

UPMC, Campus Jussieu, F-75252 Paris Cedex 05, France

† Email: francois impens@yahoo.fr Phone: +55 21 2562 7902 Poster preferred.

We propose to use a rotating corrugated material plate in order to stir, through the Casimir-Polder interaction,quantized vortices in an harmonically trapped Bose-Einstein condensate. The emergence of such vortices within thecondensate appears as a genuine signature of non-trivial geometry effects on the electromagnetic vacuum fluctuationswhich fully exploits the superfluid nature of the sample. We calculate the exact non-perturbative Casimir-Polderpotential, valid to all orders of the corrugation amplitude, felt by the atoms in front of the grating and show thatthe resulting quantum vacuum torque is strong enough to provide a contactless transfer of angular momentum to thecondensate and generate quantized vortices under realistic experimental conditions at separation distances around3µm. This work has been published on the arXiv[1].

FIG. 1: Proposed experimental setup.

[1] Francois Impens, Ana M. Contreras-Reyes, Paulo A. Maia Neto, Diego A. R. Dalvit, Romain Guerout, AstridLambrecht, and Serge Reynaud, e-print arXiv:1007.1657 (2010).

Quantum process tomography with coherent states

Saleh Rahimi-Keshari, Artur Scherer, Ady Mann, Ali Razakhani, A. I. Lvovsky, Barry C. Sanders.

Institute for Quantum Information Science, University of Calgary, Calgary, Alberta, Canada, T2N 1N4

srahimik@ucalgary.ca

Assembling a complex quantum optical information processor requires precise knowledge of the properties of each of its components, i.e., the ability to predict the effect of the components on an arbitrary input state. This gives rise to a quantum version of the famous “black box problem”, which is addressed by means of “quantum process tomography” (QPT). In this presentation, I introduce a new technique for characterizing quantum optical processes based on probing unknown quantum processes with coherent states. The original proposal [M. Lobino et al., Science 322, 563 (2008)] uses a filtered Glauber-Sudarshan decomposition to determine the effect of the process on an arbitrary state. A distinctive feature of our new method is that it obviates the need to filter the Glauber-Sudarshan representations for states. Thus, it significantly simplifies the procedure and enhances its application also to multi-mode and non-trace-preserving processes. We illustrate our findings with a set of examples, in which, by knowing the effect of some of the fundamental quantum optical processes on coherent states, we analytically derive their process tensors in the Fock basis. Moreover, to address resource vs accuracy trade-off in practical applications, we show that the accuracy of process estimation scales inversely with the square root of photon-number cutoff (as a reasonable physical resource).

THEORETICAL STUDY OF CAVITYLESS LASING WITH COLD ATOMS

Vitalie Eremeev, Miguel Orszag

Facultad de Fisica, Pontificia Universidad Catolica de Chile Av. Vicuña Mackenna 4860, Santiago, Chile Tel: (56 2) 3541684, Fax: (56 2) 5536468

E-mail: veremeev@fis.puc.cl

ABSTRACT

Recently an experimental realization of cavity lasing with cold atoms as gain medium was

reported [1]. This study is a promising step towards to the realization of a cavityless laser

(random laser) with cold atoms. Concerning to the experimental results obtained for Mollow

gain mechanism with cold atoms in the cavity we have considered an adequate theoretical

description [2] based on the model described the dressed-state lasers [3]. By using some physical

concepts similar to the cavity laser with cold atoms we develop a theoretical model for cavityless

laser. The main difference of the random lasing from the usual cavity lasing is related to the

uncertainty of the lasing modes, because in the case of cavityless or even open-cavity systems

there is no clearness of the normal modes and the complex processes as multi-scattering of the

photons in the disordered medium are sophisticated for description. In particular the gain and

losses mechanisms of the laser field in cavityless lasing depends strongly on the experimental

configuration, nevertheless we try to build a theory based on more general concept acceptable

for random lasing systems considering the methodology for the field quantization described in

[4]. Using this idea we develop the master equation for the field-atom system and in the

semiclassical approach describe some basic characteristics of the laser process. A forward-

looking objective for this problem is to use the quantum treatment for studying the coherence

properties of the field.

References: [1] W. Guerin, F. Michaud, R. Kaiser, Phys. Rev. Lett. 101, 093002 (2008). [2] W. Guerin, N. Mercadier, F. Michaud et al, J. of Optics 12, 024002 (2010). [3] J. Zakrzewski, M. Lewenstein and T.W. Mossberg, Phys. Rev. A 44, 7717–31 (1991). [4] G. Hackenbroich, C. Viviescas and F. Haake, Phys. Rev. A 68, 063805 (2003).

On  the  Relativistic  Invariance  of  Entanglement  

Esteban  Castro-‐Ruiz1,2    and    Eduardo  Nahmad-‐Achar2  

1School  of  Sciences,  National  University  of  Mexico  (UNAM)  ,  04510  Mexico  D.F.  

2Institute  for  Nuclear  Sciences,  National  University  of  Mexico  (UNAM),  04510  Mexico  D.F.  

 

Abstract  

Measurement  on  one  part  of  an  entangled  system  changes  the  probability  of  outcome  of  measurements  on  the  second  part  of  the  system,  according  to  quantum  mechanics.    This  analysis  assumes  a  time-‐ordering  of  the  events,  a  concept  which  is  not  Lorentz  invariant  for  

spatially  separated  events,  according  to  special  relativity.  

In  this  work,  the  properties  under  a  Lorentz  boost  of  a  pair  of  spin-‐1  massive  particles  are  studied,  with  spin  and  momentum  as  the  sole  degrees  of  freedom  of  the  system.    Different  

cases  for  entanglement  of  spin,  or  momentum,  or  even  starting  from  a  non-‐entangled  state,  are  considered,  and  it  is  shown  that  the  entanglement  can  be  transferred  between  the  different  degrees  of  freedom  depending  on  the  observer.  

Spontaneous-emission-induced frequency shift; a light shift from coherent driveof a single photon.

D. G. Norris1, A. D. Cimmarusti1, J. A. Crawford, L. A. Orozco1, P. Barberis-Blostein1,2,H. J Carmichael1,3

1Joint Quantum Institute, Department of Physics and National Institute of Standards andTechnology, University of Maryland, College Park, MD 20742, United States.

2Instituto de Investigacion en Matematicas Aplicadas y en Sistemas, Universidad NacionalAutonoma de Mexico, Mexico, DF 01000, Mexico.

3Department of Physics, University of Auckland, Private Bag 92019, Auckland, NewZealand.

Light shifts are a result of the atom-light coupling and are fundamental for the manipulationand control of atoms. Their effects in a multiplet of sub-levels in the ground state is welldetermined and for alkali atoms in the high hyperfine level the Zeeman separation decreaseswith increasing light level. We present a light shift of the Zeeman separation in the upperhyperfine level of the ground state that increases with increasing light level. It is caused bythe frequent interruptions due to quantum jumps of a few atoms inside an optical cavity whichhas two orthogonal polarization modes. Driving one mode and monitoring the fluctuationson the second, allow for the observation of shifts of hundreds of kiloHertz with a singlephoton in the cavity.

Work supported by NSF, CONACYT, Mexico, and the Marsden Fund of RSNZ.

1

Unambiguous discrimination of pure quantum states

Janos A. BergouDepartment of Physics and Astronomy, Hunter College of the City

University of New York, 695 Park Avenue, New York, NY 10065, USA

Abstract

State discrimination is an important paradigm inquantum information processing. It is the final stagein any QKD protocol and, more generally, it constitutesthe read-out of information encoded in a quantum sys-tem (for recent reviews on the subject, see [1, 2]). Overthe years, two main strategies emerged: discriminationwith minimum error [3] and unambiguous discrimination[4]. In this talk the focus is on the latter.

Unambiguous discrimination among N > 2 pure statesis one of the longest standing unsolved problems in quan-tum information. The problem of unambiguous discrimi-nation between two pure non-orthogonal quantum stateswas introduced and solved in [4–7]. The natural gen-eralization to the case of discriminating among N > 2states was first addressed by Peres and Terno who gavenumerical solutions for some special cases of discrimi-nating among three states [8]. Chefles showed that thesufficient and necessary condition for unambiguous dis-crimination among N states is that the states have to belinearly independent [9]. Sun et al. studied the case ofthree states when the pairwise overlaps among the statesare assumed to be real and at least two of them are equalin magnitude [10]. Recent progress was made by relatingthe unambiguous discrimination to semidefinite program-ing, and by developing a partial geometric view for theproblem and obtaining more solutions for special cases[11–13].

In this talk, we develop a complete geometric view

that, in one compact picture, encompasses all aspectsof the problem: linear independence of the states, posi-tivity of the detection operators, and leads to a graphicmethod for finding and classifying the optimal solutions[14]. We illustrate it on the example of three states andalso show that the problem depends on an invariant com-bination, the Berry phase, of the phases of the complexinner products. For arbitrary inner products and priorprobabilities only numerical solutions are possible butthe features of the solution are universal, they hold forany value of the Berry phase. We, therefore, present thecomplete analytical solution for the case when the Berryphase is either zero or π. The corresponding optimal fail-ure probability exhibits full permutational symmetry fora large range of the parameters. However, when the pa-rameters have very different values, a bifurcation takesplace, which is analogous to a second-order symmetry-breaking phase transition. At a particular value of theparameters the optimal failure probability becomes bi-valued: a second, less symmetric solution branches awayin a continuous way from the symmetric one and it is op-timal in the new regime. The optimum measurement isa general measurement (POVM) and we also obtain theexplicit expression for the POVM elements that performthe optimal unambiguous state discrimination strategy.We conclude with a discussion of the generalization of ourresults to the discrimination of more than three states.Time permitting we will also give a brief overview of re-cent progress on other open problems in unambiguousstate discrimination.

[1] S. M. Barnett and S. Croke, Advances in Optics andPhotonics 1, 238 (2009).

[2] J. A. Bergou, Journal of Modern Optics 57, 160 (2010).[3] C. W. Helstrom, Quantum Detection and Estimation

Theory (Academic Press, 1976).[4] I. D. Ivanovic, Phys. Lett. A 123, 257 (1987).[5] D. Dieks, Phys. Lett. A 126, 303 (1988).[6] A. Peres, Phys. Lett. A 128, 19 (1988).[7] G. Jaeger and A. Shimony, Phys. Lett. A 197, 83 (1995).[8] A. Peres and D. R. Terno, J. Phys. A 31, 7105 (1998).

[9] A. Chefles, Phys. Lett. A 239, 339 (1998).[10] Y. Sun, M. Hillery, and J. A. Bergou, Phys. Rev. A 64,

022311 (2001).[11] M. A. Jafarizadeh, M. Rezaei, N. Karimi andA. R. Amiri,

Phys. Rev. A 77, 042314 (2008).[12] S. Pang and S. Wu, Phys. Rev. A 80, 052320 (2009).[13] H. Sugimoto, T. Hashimoto, M. Horibe, andA. Hayashi,

arXiv[quant-ph]:1007.5112 (2010).[14] U. Futschik, E. Feldman, and J. A. Bergou, in prepara-

tion.

Optimized measurement for the maximum-confidence discriminationof mixed quantum states

Ulrike Herzog

Institute of Physics, Humboldt University Berlin, D 12489 Berlin, Germanyemail: ulrike.herzog@physik.hu-berlin.de

Quantum state discrimination lies at the heart of quantum communicationand quantum cryptography. In the standard problem a quantum system isprepared with known prior probability in a certain state that belongs to afinite set of possible states. The task is to infer from a single measurement inwhich state the system was prepared. Since non-orthogonal quantum statescannot be distinguished perfectly, various optimized discrimination strategieshave been developed. One of these is unambiguous discrimination, where errorsare not allowed, at the expense of admitting inconclusive results where themeasurement fails.

Unambiguous discrimination is only possible for pure states that are linearlydependent, or for mixed states described by density operators with differentsupports. For cases when one ore more states in the given set cannot be unam-biguously discriminated, the strategy of state discrimination with maximumconfidence has been introduced [1] which can be considered as a generalizationof unambiguous discrimination and contains the latter as a special case.

Like for unambiguous discrimination, also for maximum-confidence discrimi-nation an optimized measurement exists where the probability of inconclusiveresults takes a minimum. Recently we derived the optimized measurementwhich discriminates two mixed quantum states with maximum confidence andminimum failure probability, provided that for the given states the rank ofthe detection operators associated with the conclusive measurement outcomesdoes not exceed unity [2]. In the present contribution this work is extended.In particular, the case of higher-rank detection operators is considered and theproblem is generalized to the optimized maximum-confidence discriminationof more than two mixed states. The implementation of the measurement isalso briefly addressed.

[1] S. Croke, E. Andersson, S. M. Barnett, C. R. Gilson and J. Jeffers, Phys.Rev. Lett. 96, 070401 (2006)

[2] U. Herzog, Phys. Rev. A 79, 032323 (2009)

Non-orthogonal Mutually unbiased basis

Isabel Sainz, A.B. Klimov, and L. Roa

Departamento de Física, Universidad de Guadalajara, Revolución 1500, Guadalajara, Jalisco 44420, México

e.mail: klimov@cencar.udg.mx

It is well known that when the dimension of the Hilbert space is a prime number (p), it is always possible to construct p+1 orthogonal mutually unbiased bases (MUB). In this case the measured probabilities in these bases completely determine de density operator of the system, which allows developing an optimal quantum tomographyc procedure.

However, when only a limited access to the full state space is granted, one should apply quantum tomography with non-orthogonal bases.

In this work we consider a linearly independent and non-orthogonal set of normalized states in a p-dimensional Hilbert space, such that the scalar product between any two different states of the set is a real constant λ. Then, we obtain the bi-orthogonal correspondent basis, such that the scalar product between these two bases is orthogonal. These bases are eigenstates of some non-unitary and cyclic operator Z and its hermitic conjugate respectively.

In close analogy with the orthogonal case, we introduce a unitary and cyclic operator X that forms a dual pair with operator Z, i.e. ZX=ωXZ. We then find another p-1 bases whose elements corresponds to the eigenstates of the monomials 𝑍 𝑋, s=1,…,p-1. And their corresponding set of bi-orthogonal bases is also constructed. It results that the bases are mutually unbiased with their corresponding bi-orthogonal bases.

The unbiasedness can be use for an optimal reconstruction of a density matrix. The main idea consists in expanding the density matrix on the bi-orthogonal projectors, while measurements are accomplished in the bases.

The orthogonal and near to parallel limit are studied.

Title: Pulling out Small Signals with Weak Values Authors: John C. Howell, David Starling, P. Benjamin Dixon, Andrew N. Jordan,

Nathan Williams and Justin Dressel Department of Physics and Astronomy, University of Rochester, Rochester NY

14627 Weak values have proven to be both a fruitful and controversial field of study. While initially trying to understand the uncertainty principle in quantum mechanics, the ideas have recently branched out to precision measurements. In this talk, I will discuss recent advances in our lab, in which we have observed sub picometer deflections of a laser beam (equivalent to measuring a hairs breadth at the distance of the moon), characterized the rather surprising signal noise ratio, demonstrated a broadband high sensitivity spectrometer and violated a Leggett-Garg inequality using weak measurements of entangled photons.

Figure: a collimated optical beam is fed into a Sagnac interferometer; a compensator (SBC) placed in one of its arms adds a relative phase shift between beams traveling clockwise and counterclockwise. A piezoelectric actuator is used to rotate one of the mirrors, leading to a deflection of the counterpropagating beams in opposite directions at the output port. Interference of the beams leads to an amplified transverse deviation of the signal at the detector. The figure shows the experimental setup for the precision deflection measurement. A small measurement of the which-path uncertainty of the photon is achieved by a small deflection of a piezo-driven mirror and a split detector at the output of the interferometer. A careful analysis of the signal to noise ratio showed that we could achieve approximately 1 picoradian/Hz-1/2 sensitivity, which is over 50 times better than is possible by removing the 50/50 beamsplitter causing the interference to disappear. I will also report on some very recent results discussing macrorealism and entanglement.

Entanglement evolution for quantum trajectories

Dominique SpehnerInstitut Fourier, Universite Joseph Fourier and CNRS,

BP 74, 38402 Saint Martin d’Heres, France and

Laboratoire de Physique et Modelisation des Milieux Condenses,

Universite Joseph Fourier and CNRS, BP 166, 38042 Grenoble, France

Entanglement is a key resource in quantum information. It can be destroyed or sometimes createdby interactions with a reservoir. In recent years, much attention has been devoted to the phenom-ena of entanglement sudden death and sudden birth, i.e., the sudden disappearance or revival ofentanglement at finite times resulting from a coupling of the quantum system to its environment [1].Entanglement sudden death occurs for certain initial states only or for all entangled initial states,depending on whether the system relaxes to a steady state belonging to the boundary of the setof separable states (e.g. to a separable pure state for baths at zero temperature) or to its interior.Entanglement sudden birth can occur when the two parts of a bipartite system are coupled to a com-mon reservoir [2]. In this talk, we will analyze the evolution of the entanglement of noninteractingqubits coupled to reservoirs under monitoring of the reservoirs by means of continuous measure-ments. Because of these measurements, the qubits remain at all times in a pure state, which evolvesrandomly. To each measurement result (or “realization”) corresponds a quantum trajectory in theHilbert space of the qubits. We will show that for two qubits coupled to independent baths sub-jected to local measurements, the average of the qubits’ concurrence over all quantum trajectoriesalways decays exponentially [3]. The corresponding rate depends on the measurement scheme only.This result contrasts with the entanglement sudden death phenomenon exhibited by the qubits’density matrix in the absence of measurements. Our analysis applies to arbitrary quantum jumpdynamics (photon counting) as well as quantum state diffusion dynamics (homodyne or heterodynedetections) in the Markov limit. It implies that, if the density matrix exhibits entanglement suddendeath and there exists a measurement scheme such that the average concurrence over all quantumtrajectories be equal to the density matrix concurrence at all times, then this scheme must nec-essary involve nonlocal (joint) measurements on the two reservoirs [4]. We will discuss the bestmeasurement schemes to protect the entanglement of the qubits, i.e., the schemes maximizing theaverage concurrence. In specific examples such as pure dephasing and baths at infinite temperature,a perfect protection can be obtained; this means that maximally entangled states at t=0 remainmaximally entangled at all times and for all quantum trajectories. We will also analyze the case oftwo qubits coupled to a common bath. In this case, the average concurrence can vanish at discretetimes and may coincide with the concurrence of the density matrix.

[1] T. Yu and J.H. Eberly, Phys. Rev. Lett. 93, 140404 (2004); L. Diosi, in Irreversible Quantum Dynamics, Lecture Notes inPhysics 622, 157, Eds. F. Benatti and R. Floreanini (Springer, Berlin, 2003); P.J. Dodd and J.J. Halliwell, Phys. Rev. A69, 052105 (2004)

[2] D. Braun, Phys. Rev. Lett. 89, 277901 (2002); Z. Ficek and R. Tanas, Phys. Rev. A 74, 024304 (2006)[3] S. Vogelsberger and D. Spehner, arXiv:1006.1317 [quant-ph][4] H. Nha and H.J. Carmichael, Phys. Rev. Lett. 93, 120408 (2004); A.R.R. Carvalho, M. Busse, O. Brodier, C. Viviescas,

and A. Buchleitner, Phys. Rev. Lett. 98, 190501 (2007); C. Viviescas, I. Guevara, A.R.R. Carvalho, M. Busse, and A.Buchleitner, arXiv:1006.1452 [quant-ph]

Long life to quantum correlations

Sabrina Maniscalco The interaction between a quantum system and its environment causes the rapid destruction of crucial quantum properties, such as the existence of quantum superpositions and of quantum correlations in composite systems. Decoherence and dissipation induced by the environment are responsible for the extreme fragility of quantum states and are therefore considered the major enemies of quantum technologies. Is there any environment-resistant quantum property? Is there any physical system in which quantum correlations can survive, completely unaffected by the environment? After reviewing the main results on the quantum to classical transition, I will present the first evidence of the existence of a positive answer to these questions. I will show that, for a certain class of initial states, quantum correlations quantied by the discord are not destroyed by decoherence for times t < t*. In this initial time interval only classical correlations decay. For t > t*, on the other hand, classical correlations remain constant in time and only quantum correlations are lost due to the interaction with the environment. Therefore, at the transition time t* the open system dynamics exhibits a sudden transition from classical to quantum decoherence regime [1,2]. The discovery of environment-resistant quantum correlations unveils a new feature of one of the most fundamental and fascinating aspects of quantum theory and may be a key breakthrough on quantum technologies. [1] L. Mazzola, J. Piilo, and S. Maniscalco, Phys. Rev. Lett. 104, 200401 (2010). [2] Jin-Shi Xu et al., Nat. Commun. 1 (2010) 7.

Decay analysis with reservoir structures

Barry M. Garraway

Department of Physics and Astronomy, University of Sussex

Static reservoir structures coupled to simple quantum systems can be analysed by the method of "pseudomodes" [1], where the reservoir structure is replaced by an effective mode. The approach can be useful for strongly coupled, i.e. non-Markovian problems. An introduction to this theory will be given with some simple examples and recent results involving reservoir memory [2] and entanglement in the reservoir [3].

[1] B.M. Garraway, Phys. Rev. A 55, 4636 (1997). [2] L. Mazzola, S. Maniscalco, J. Piilo, K.-A. Suominen, and B.M. Garraway, Phys. Rev. A. 80, 012104 (2009). [3] C. Lazarou, B.M. Garraway, J. Piilo, and S. Maniscalco, arXiv:1008.2621

Engineering inverse power law decoherence of a qubit

Filippo Giraldi and Francesco Petruccione

Quantum Research Group, University of KwaZulu-Natal and National Institute for

Theoretical Physics, Durban, South Africa The exact dynamics of a Jaynes-Cummings model for a qubit interacting with a bath of bosons, characterized by a special form of the spectral density, is evaluated analytically. The special reservoir is designed to induce anomalous decoherence, resulting in an inverse power law relaxation, of power three half, on an evaluated long time scale. If compared to the exponential-like relaxation obtained from the original Jaynes-Cummings model for Lorentzian-type spectral density functions, decoherence is considerably hindered.

Current status of the experiment on Dynamical Casimir Effect in cavities with laser excited semiconductor mirrors

V. V. Dodonov

Instituto de Fisica, Universidade de Brasilia, Brazil

I intend to report on the theoretical analysis of recent experimental results obtained by the MIR group in Padova (Italy) in connection with the attempts to observe the Dynamical Casimir Effect (DCE) in cavities with laser excited semiconductor mirrors. In this scheme, a fast periodical motion of the cavity wall is imitated by fast changes of the conductivity in a thin semiconductor slab excited by periodical picosecond laser pulses of the micro-Joule energy. The recent experimental data concerning the parametric amplification of the classical signal in the so-called re-entrant cavity seem to be in a good agreement with the available theoretical model. This fact can be considered as an indication that the main experiment aimed at the generation of the significant number of photons from the initial quantum vacuum state can be performed soon. The optimal values of parameters giving the maximal photon generation rate (such as the power and the shape of the laser pulse, the recombination time and the mobility of carriers, the shape and dimensions of the cavity) will be discussed. Still unsolved fundamental theoretical problems will be also posed.

Dynamical Casimir effect in uniformly accelerated media

Lukasz Rudnicki, Iwo Bialynicki-Birula

Center for Theoretical Physics PAS, Al. Lotnikow 32/46, 02-668 Warsaw, Poland

Contact email address rudnicki@cft.edu.pl According to quantum theory, the vacuum is filled with virtual photons and their excitation may produce real photons. This phenomenon falls under a general category of the dynamical Casimir effect, especially when it is connected with a movement. Of course for the movement with constant velocity nothing happens because of the Lorentz invariance of the Maxwell electrodynamics. In my conference poster I am going to present analytical results of calculations of the photon density in the case of dielectric media moving with a constant acceleration (in a relativistic manner) [L. Rudnicki, I. Bialynicki-Birula, Opt. Comm. 283, 644 (2010)]. This situation is not equivalent to the celebrated Unruh effect since the photon density differs significantly from the famous black body radiation spectrum.

Information hidden in the coherence

Zdenek Hradil, J Rehacek, Luis L Sanchez Soto

Department of Optics, Palacky University, 17. listopadu 12, 77146 Olomouc, Czech Republic

hradil@optics.upol.cz

Light is a major source of information on the world around us, from the microcosmos to the macrocosmos. The present methods of detection are sensitive both to robust features, such as intensity, or polarization, and to more subtle effects, such as correlations. Here we show how wavefront detection, which allows for registering of the direction of the incoming wave flux at a given position, can be used to reconstruct the mutual coherence function when combined with some techniques previously developed for quantum information processing. Amazingly, the mathematical formulation behind these scanning devices has strong implications in fields as diverse as classical optics, visual processing, or exploration of the Universe. This approach involves the notions of simultaneous measurement of noncommuting observables and quantum tomography, which have been already adopted for assessing nonclassical affects in the realm of quantum world. The purpose of the talk is to point out that standard wavefront measuring systems may be underrated and do not fully exploit the registered data. Indeed, by resorting to methods of tomographic reconstruction, we show that these devices allow for an evaluation of the mutual coherence function of the signal. The main purpose of our contribution is not to present a detailed account of the method or to work out all possible applications, but rather to trigger a scientific discussion on the ultimate limits on information processing, even with classical wavefields.

Preparing the bound instance of entanglement

Carlos Pineda, J. DiGuglielmo, A. Samblowski, B. Hage, J. Eisert, R.

Schnabel

IFUNAM Entanglement is the feature of quantum mechanics that renders it crucially different from any classical statistical theory. Among the possibly most remarkable aspects of quantum entanglement is that it comes in "free'' and "bound'' instances. Bound entangled states require entangled states in preparation but, once realized, no free entanglement and therefore no pure maximally entangled pairs can be locally regained. Their existence hence certifies an intrinsic irreversibility of entanglement in nature and suggests a connection with a thermodynamical picture of entanglement. In this work, we present a first experimental unconditional preparation and detection of a bound entangled state of light. We use convex optimization to identify regimes rendering the bound character of continuous-variable entanglement well certifiable and realize an experiment that continuously produced a bound entangled state with an extraordinary significance of more than ten standard deviations away from both separability and distillability. This platform allows for the efficient preparation of multi-mode entangled states of light with various applications in quantum information, quantum state engineering and metrology.

Measurement of the Spiral Spectrum of Entangled Two-Photon States

H. Di Lorenzo Pires, H. C. B. Florijn, and M. P. van Exter

Huygens Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands

Author e-mail address: pires@molphys.leidenuniv.nl

Since the existence of quantum OAM correlations between photon pairs was first demonstrated [1], an

increasing effort is being devoted to manipulate and measure these states. In this context, a full character-

ization of the OAM correlations is essential. We consider rotationally-symmetric geometries and write the

entangled two-photon state as |ψ〉 =∑+∞

l=−∞

√Pl|l〉s| − l〉i The main question we want to address experi-

mentally is: what is the precise form of the OAM spectra of down-converted photons? In other words: what

are the probabilities Pl of different l modes, where l represents the photon topological winding number?

The studied source comprises a periodically-poled KTP crystal pumped at λ = 413 nm and tuned to

produce frequency-degenerate (λ = 826 nm) photons in a collinear geometry. Temperature tuning allows one

to modify the collinear phase mismatch ϕ and thereby change the spatial profile of the generated two-photon

field as well as its OAM distribution. We route the two photons through a Mach-Zehnder interferometer

with an image rotator in one of its arms and measure the visibility of the two-photon interference versus

the rotation angle. A Fourier decomposition is used to recover the OAM spectrum. A similar technique

was proposed for the analysis of a one-photon field [2] and applied to the analysis of a two-photon in a

constricted non-collinear geometry [3]. Our collinear geometry doesn’t restrict the two-photon field in any

way and allows us to record the spiral spectrum of the total generated field [4]. The use of bucket detectors

is essential in this respect.

We also show that the phase-matching conditions can be used as a tool to efficiently boost the number of

entangled modes (quantified by the azimuthal Schmidt number Kaz ≡ 1/∑

lP 2

l), flatten the spectral profile,

and increase the conversion efficiency (see Fig.).

The reported results are, to the best of our knowledge, the first measurements where the entire down-

converted cone is considered and where the detection geometry does not shape the spectrum nor limits its

dimensionality Kaz.

ϕ

ϕ = 1

ϕ = −9

Figure 1: The effect of phase mismatch ϕ on the modal decomposition Pl (left) and the azimuthal Schmidt number Kaz

(right). The parameter ϕ is related to the far-field SPDC rings via the phase-matching function sinc(cθ2 + ϕ). The inset in therighthand figure shows the measured visibilities V (θ), whose Fourier transforms provides the OAM spectrum.

[1] A. Mair et al., “Entanglement of the orbital angular momentum states of photons”, Nature 412, 313 (2001).

[2] R. Zambrini and S. Barnett, “Quasi-intrinsic angular momentum and the measurement of its spectrum”, Phys. Rev. Lett.96, 013901 (2006).

[3] W.H. Peeters, E.J.K. Verstegen, and M.P. van Exter, “Orbital angular momentum analysis of high-dimensional entangle-ment”, Phys. Rev. A 76, 042302 (2007).

[4] H. Di Lorenzo Pires, H.C.B. Florijn, and M.P. van Exter, “Measurement of the spiral spectrum of entangled two-photonstates”, Phys. Rev. Lett. 104, 020505 (2010).

Optical realization of a novel factorization algorithm 1

Vincenzo TammaUniv. of Maryland, Baltimore County; Univ. degli Studi di Bari;

tammav1@umbc.edu

The security of codes, for example in credit card and government information, relies on the fact that thefactorization of a large integer number N is a rather costly process on a classical digital computer. Such asecurity is endangered by the Shor’s algorithm which employs entangled quantum systems to find, with apolynomial number of resources, the period of a function which is connected with the factors of N . We cansurely expect a possible future realization of such a method for large numbers, but so far the period of Shor’sfunction has been only computed for the number 15.

Inspired by Shor’s idea, our work aims to methods of factorization based on the periodicity measurementof a given continuous periodic “factoring function” which is physically implementable using an analoguecomputer.

In particular, we have focused on both the theoretical and the experimental analysis of Gauss sums withcontinuous arguments leading to a new factorization algorithm. The procedure allows, for the first time,to factor several numbers by measuring the periodicity of Gauss sums performing first-order “factoring”interference processes.

We experimentally implemented this idea by exploiting polychromatic optical interference in the visiblerange with a multi-path interferometer, and achieved the factorization of seven digit numbers (see figure).For each number N to factorize, the corresponding trial factors associated with the brightest wavelengths(maxima in the interferogram) are the factors.

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1Ph.D. Thesis: “Theoretical and experimental study of a new algorithm for factoring numbers” by V. Tamma

Localized photon states

Margaret Hawton

Lakehead University 955 Oliver Road

Thunder Bay, Ontario, Canada P7B 5E1

Email: margaret.hawton@lakeheadu.ca The theoretical difficulties associated with the concept of photon position have been examined since the early days of quantum mechanics. The most severe mathematical limitation is that, according to the Paley-Weiner theorem, a converging (or diverging) photon pulse must have subexponential tails and this precludes exact localization. I have calculated the the positive operator valued measure (POVM) for a photon counting array detector and found that it equals the photon flux density operator integrated over pixel area and measurement time [M. Hawton, arxiv.org/abs/1007.0460, to be published in Phys. Rev. A]. In spite of the nonlocalizability of the incoming photon, the POVM derived is a sum over projection operators onto exactly localized states. The probability density to count a photon was found to equal the absolute square of the wave function provided the photon wave function is defined as the projection of its state vector onto the localized basis states. There are in principle many ways to construct a POVM since any partition of the identity is allowed, but the exactly localized states arose naturally in this calculation. Collapse was found to be to the electromagnetic vacuum rather than to a localized state, in violation the text book rules of quantum mechanics but compatible with the theory of generalized observables and the nonlocalizability of an incoming photon. I will discuss the relationship of exactly localized photon states to photodetection and to scattering of a single photon by a nanoparticle. In the latter case incoming and outgoing waves are summed so a scattered photon can be approximately localized for an instant.

Witness for initial system-environment correlations in open system dynamics

E.-M. Laine1, J. Piilo1,H.-P. Breuer2

1Turku Center for Quantum Physics, Department of Physics and Astronomy, Universityof Turku, FI-20014 University of Turku, Finland2Physikalisches Institut, Universität Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg,Germanyemail: emelai@utu.fi

We study the evolution of a general open quantum system when the system and its en-vironment are initially correlated. We show that the trace distance between two states ofthe open system can increase above its initial value, and derive tight upper bounds for thegrowth of the distinguishability of open system states. This represents a generalization ofthe contraction property of quantum dynamical maps. The obtained inequalities can beinterpreted in terms of the exchange of information between the system and the environ-ment, and lead to a witness for system-environment correlations which can be determinedthrough measurements on the open system alone. We introduce a measurement schemeto detect initial correlations, which neither requires a knowledge of the structure of theenvironment or of the system-environment interaction, nor a full knowledge of the initialsystem-environment state.

[1] E.-M. Laine, J. Piilo, H.-P. Breuer, arXiv: 1004.2184 [quant-ph]

Simulating Quantum Systems in Biology, Chemistry, and PhysicsB. P. Lanyon1, J. D. Whitfield2, G. G. Gillett1, M. E. Goggin1, M. P. Almeida1, I. Kassal2,

J. D. Biamonte2, M. Mohseni2, B. J. Powell1, M. Barbieri1, A. Aspuru-Guzik2, & A. G. White1

1Department of Physics, University of Queensland, Brisbane QLD, Australia2Department of Chemistry, Harvard University, Cambridge MA, USA

agx.white@gmail.com http://quantum.info/

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FIG. 1: Measured results from photonic quantum algorithm: H2potential energy curves in a minimal basis. Each point is ob-tained using a 20-bit photonic iterative-phase-estimation algorithm(IPEA) and employing n=31 samples per bit (repetitions of each it-eration). Every case was successful, achieving the target precision of±(2−20×2π) Eh∼10−5 Eh. Curve G (E3) is the low (high) eigenvalueof H(1,6). Curve E1 is a triply degenerate spin-triplet state, correspond-ing to the lower eigenvalue of H(3,4) as well as the eigenvalues H(2) andH(5). Curve E2 is the higher (singlet) eigenvalue of H(3,4). Measuredphases are converted to energies E via E=2πφ+1/r, where the lastterm accounts for the proton-proton Coulomb energy at atomic separa-tion r, and reported relative to the ground state energy of two hydrogenatoms at infinite separation. Inset a): Curve G rescaled to highlight thebound state. Inset b): Example of raw data for the ground state energyobtained at the equilibrium bond length, 1.3886 a.u.. The measured bi-nary phase is φ=0.01001011101011100000 which is equal to the exactvalue, in our minimal basis, to a binary precision of ±2−20.

In principle, it is possible to model any physical systemexactly using quantum mechanics; in practice, it quicklybecomes infeasible. Recognising this, Richard Feynmansuggested that quantum systems be used to model quan-tum problems [1]. For example, the fundamental problemfaced in quantum chemistry is the calculation of molecu-lar properties, which are of practical importance in fieldsranging from materials science to biochemistry. Withinchemical precision, the total energy of a molecule as wellas most other properties, can be calculated by solving theSchrodinger equation. However, the computational re-sources required to obtain exact solutions on a conventionalcomputer generally increase exponentially with the numberof atoms involved [1, 2]. In the late 1990’s an efficient algo-rithm was proposed to enable a quantum processor to cal-culate molecular energies using resources that increase onlypolynomially in the molecular size [2–4]. Despite the manydifferent physical architectures that have been explored ex-perimentally since that time—including ions, atoms, super-conducting circuits, and photons—this appealing algorithmhas not been demonstrated to date.

Here we take advantage of recent advances in photonicquantum computing [5] to present an optical implementa-tion of the smallest quantum chemistry problem: obtainingthe energies of H2, the hydrogen molecule, in a minimalbasis [6]. We perform a key algorithmic step—the itera-tive phase estimation algorithm [7–10]—in full, achievinga high level of precision and robustness to error. We imple-ment other algorithmic steps with assistance from a classi-cal computer, and explain how this non-scalable approach could be avoided. We also provide new theoretical results which laythe foundations for the next generation of simulation experiments using quantum computers.

We also report on our recent results in simulating quantum systems in material science—phase transitions in topologicalinsulators—and in biology—light-harvesting molecules in photosynthesis. Together this body of work represents early exper-imental progress towards the long term goal of exploiting quantum information to speed up calculations in biology, chemistryand physics.

[1] R. P. Feynman, International Journal of Theoretical Physics 21, 467 (1982).[2] S. Lloyd, Science 273, 1073 (1996).[3] D. Abrams and S. Lloyd, Physical Review Letters 79, 2586 (1997).[4] C. Zalka, Proceedings of the Royal Society of London A 454, 313 (1998).[5] B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G.

White, Nature Physics 5, 134 (2009).[6] B. P. Lanyon, J. D. Whitfield, G. G. Gillet, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri,

et al., Nature Chemistry 2, 106 (2010).[7] K. R. Brown, R. J. Clark, and I. L. Chuang, Physical Review Letters 97, 050504 (2006).[8] D. A. Lidar and H. Wang, Physical Review E 59, 2429 (1999).[9] A. Aspuru-Guzik, A. Dutoi, P. Love, and M. Head-Gordon, Science 309, 1704 (2005).

[10] C. R. Clark, K. R. Brown, T. S. Metodi, and S. D. Gasster, arXiv:0810.5626 (2008).

Dispersion of Entangled Photon Pairson an Ultrafast Timescale

Kevin A. O’DonnellDivisión de Física Aplicada

Centro de Investigación Científica y de Educación Superior de EnsenadaCarretera Ensenada-Tijuana Numero 3918, Zona Playitas

Ensenada, Baja California, C.P. 22860 México

The temporal dispersion of entangled photon pairs has long been of interest. For example, nonlocal dispersion cancel-lation of the two-photon state itself has been theoretically discussed [1], and the dispersion cancellation occurring inthe Hong-Ou-Mandel interferometer has been experimentally demonstrated [2]. However, direct observation of effectsof dispersion on the two-photon state, as measured through the time-resolved coincidence rates of detected photonpairs, has been severely limited by poor electronic timing resolution (&0.1 ns) [3].

Here, to overcome this limitation, a new, dispersion-sensitive experimental approach is taken in which the entangledphoton pairs are upconverted in a nonlinear crystal [4]. In particular, a delay τ is introduced between the signal andidler modes, and the upconverted photon rate is measured as a function of τ [5]. The temporal resolution is determinedby the positioning accuracy of the mirror producing the delay, and is thus . 1 fs. The approach is analogous to thattaken in the common autocorrelation method of ultrafast laser pulse characterization.

In the experiments, the focused beam of a pump laser (532 nm wavelength, power 1 W, single-mode) produced spon-taneous parametric downconversion in a periodically-poled, lithium niobate crystal of 5 mm length. A 2◦ half-anglecone of downconversion was collimated by a lens, sent through a sequence of 4 near-Brewster prisms for dispersioncompensation, and focused to upconvert in a second, identical nonlinear crystal. Before the crystal, one half of thedownconversion cone (signal side) was reflected from a piezoelectrically-positioned mirror, which introduced the de-lay τ , while the other (idler) side was reflected from a fixed, coplanar mirror. In Fig. 1 it is seen that the optimum casepresents a full-width at half-maximum of only 26.7 fs, with secondary maxima near τ=±45 fs. In the other two casesshown, equal group delay dispersion is added to both the signal and idler modes, with the effect that the peak falls andwidens. Other possibilities to be discussed include unequal dispersion in the signal and idler modes, and studies ofpartial dispersion cancellation as seen in the upconversion rate.

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Fig. 1. Upconverted photon rates (s−1) as a function of signal/idler delay τ for: (a) optimized dispersion, (b) −115 fs2 additional dispersion, and(c) +198 fs2 additional dispersion in both signal and idler modes.

References1. J. D. Franson, "Nonlocal Cancellation of Dispersion," Phys. Rev. A 45, 3126-3132 (1992).2. A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, "Dispersion Cancellation in a Measurement of the Single-Photon Propagation Velocity in

Glass," Phys. Rev. Lett. 68, 2421-2424 (1992).3. A. Valencia, M. V. Chekhova, A. Trifonov, and Y. Shih, "Entangled Two-Photon Wave Packet in a Dispersive Medium," Phys. Rev. Lett. 88,

183601 (2002).4. B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, "Nonlinear Interactions with an Ultrahigh Flux of Broadband Entangled Photons,"

Phys. Rev. Lett. 94, 043602 (2005).5. K. A. O’Donnell and A. B. U’Ren, "Time-Resolved Upconversion of Entangled Photon Pairs," Phys. Rev. Lett. 103, 123602 (2009).

Observation of quantum emitters injected in tissue: a novel strategy to restrict diffusion

through narrow gaps

Veneranda Garcés *, Tatiana Krasieva

+, and Kevin A. O’Donnell

*

* División de Física Aplicada, Centro de Investigación Científica y de Educación Superior de Ensenada, Carretera Ensenada-Tijuana, Número 3918, Zona Playitas, Ensenada, Baja California, México C. P. 22860

+ Beckman Laser Institute and Medical Clinic, Univ. of California, Irvine, 1002 Health Sciences Rd., East, Irvine, CA 92612

vgarces@cicese.mx

Quantum dots (QDs) are semiconductor nanocrystals that act as quantum emitters. They promise to be useful in

current research areas, such as quantum information [1] and optical nanosensors [2], where the observation of single

QDs can be useful. The excitons in these materials are electron-hole pairs, which behave in a quantized way and are

relatively straightforward to control and detect optically. Their emission wavelengths depend on their size due to

quantum confinement effects. Moreover, their composition, shape, and sizes can be engineered to produce a wide

range of desired properties. Observation of QDs is difficult due to their Brownian motion. Various techniques, such

as optical tweezers, have been used to observe them. The sizes of QDs are of the order of few nanometers, which

makes it difficult to trap them for further experiments or investigations.

In this work we discuss a straightforward method to observe them inside a fresh biological sample. Approximately

70 nm sized nonfunctionalized QDs were injected into animal tissue. High-resolution images of collagen and elastic

fibers were acquired with confocal multiphoton microscopy. Collagen second harmonic generation (SHG) and two-

photon excited fluorescence (TPEF) of QDs were simultaneously excited by a tunable femtosecond laser, which

produced images having a significant improvement in the 3D reconstruction of the sample. Images taken in real time

demonstrated that QDs were diffusing inside different tissue components, but they became trapped by the gaps

between collagen fibers or compact muscle. The images show that the QDs were not uptaken by the cells located in

the tissue, but were instead strongly bound to their membranes. These immobilized bounded QDs have allowed a 3D

image reconstruction of the components of the structural tissue. Clearly crosslinked collagen fibers of connective

tissue were observed even when the fibers changed direction. The resultant images have shown that the SHG and

TPEF signals obtained simultaneously provided complementary structural information. This information can inspire

further development of engineered tissue samples, where crosslink, size and separation between collagen and elastic

fibers could be controlled. More advance engineered tissue samples with a desired collagen structural pattern, as in

a net, could allow the trapping a single quantum dot in each empty volume.

Furthermore, the samples studied here can lead to further experiments on, for instance, quantum entanglement

between pairs of QDs or studies of quantum optical excitation. Although we used multiphoton microscopy to image

the samples, it is also possible to obtain the images with a single-photon imaging system which can be simpler to

integrate into a portable system. Finally, these samples can also be used for teaching proposes because they provide

a visual demonstration of fundamental concepts that can be difficult for many students.

References

1. D. Gammon and D. G. Steel, “Optical studies of single quantum dots,” Physics Today, October (2002).

2. P. Alivisatos, “The use of nanocrystals in biological detection,” Nature Biotechnology, 22, 47-52 (2004).

Integrated quantum photonics

D Bonneau, P Kalasuwan, A Laing, JCF Matthews, A Peruzzo, K Poulios, P Shadbolt, JPHadden, JP Harrison, AC Stanley-Clark, L Marseglia, Y-LD Ho, BR Patton, JG Rarity, P Jiang,

M Halder, M Lobino, A Politi, M Rodas Verde, X-Q Zhou, MG Thompson, and JL OBrien∗

Centre for Quantum Photonics, H. H. Wills Physics Laboratory & Department of Electrical and Electronic Engineering,University of Bristol, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB, UK

We describe recent developments in integrated quantum photonics, including waveguide circuitsto implement quantum logic operations, quantum metrology and quantum walks.

Quantum information science has shown that harness-ing quantum mechanical effects can dramatically improveperformance for certain tasks in communication, compu-tation and measurement. Of the various physical sys-tems being pursued, single particles of light - photons -are often the logical choice [1]. In addition to single pho-ton sources and detectors, photonic quantum technolo-gies will rely on sophisticated optical circuits involvinghigh-visibility classical and quantum interference. Al-ready a number of optical quantum circuits have beenrealized for quantum metrology, lithography, quantumlogic gates, and other entangling circuits. However, thesedemonstrations have relied on large-scale (bulk) opticalelements bolted to large optical tables, thereby makingthem inherently non-scalable and confining them to theresearch laboratory. In addition, many have required thedesign of sophisticated interferometers to achieve the sub-wavelength stability required for reliable operation.

The implementation of quantum optic integrated cir-cuits not only dramatically reduces the footprint of quan-tum circuits, but allows unprecedented stability and con-trol of the optical path length; this reveals the possibilityfor realizing previously unfeasible large scale quantumcircuits [2]. We recently demonstrated silica on siliconcircuits that implement key components for quantum in-formation, including CNOT gates [3] and the circuit atthe basis of any single-qubit operation [4]. These compo-nents show promising progresses toward fault toleranceoperation [5]. We used integrated waveguides to imple-ment a circuit that performs a compiled version of Shor’squantum algorithm [6] to factorize 15.

Here report demonstration of a silica-on-silcon waveg-uide device for quantum metrology applications. Thesame device is capable of heralding the two- and four-photon NOON states |20〉 + |02〉 and |40〉 + |04〉, as wellas the four-photon state |31〉 + |13〉, dependent upon theinput state and the setting of an integrated internal phase[7]. While NOON states are fragile with respect to pho-ton loss, other linear superpositions of photon numberentanglement, as the |31〉 + |13〉 state, can beat the SQLin interferometers with loss.

Quantum random walks, the quantum analogue of sta-tistical random walks, have great potential for designing

a new generation of quantum algorithms and can be re-garded as a primitive for universal quantum computa-tion. We describe our most recent results on quantumwalks of correlated particles in arrays of coupled waveg-uides [8]. The interference of two photons in the arraycan be seen as a generalization of the Hong-Ou-Mandeleffect, which leads to various patterns of correlated statis-tics dependent upon the input state. While part of themodel can be verified with classical correlation statistics,no experiment to date has been reported using quantumstates of single photons to reproduce the full quantumcorrelation behavior.

In order for linear optical quantum computing schemesto become practical an efficient source of single photons isrequired [1]. We report on the implementation of a micro-fabricated single photon source based on diamond thatallows high collection efficiency[9]. This enhancementcompares favourably to those reported from nanoscaledevices without requiring the colour centres to be nearto decohering surface effects.

The results presented here, combined with efficient sin-gle photon detectors [10], will be the building block forfuture demonstrations of quantum information with pho-tons.

∗ Electronic address: Jeremy.OBrien@bristol.ac.uk

[1] J.L. O’Brien. In Science, 318:1567, 2007.[2] J.L.O’Brien, A. Furusawa and J. Vuckovic. In Nature

Photonics, 3:687, 2009.[3] A. Politi, M.J. Cryan, J.G. Rarity, S. Yu and J.L.

O’Brien. In Science, 320:646, 2008.[4] J. C. F. Matthews, A. Politi, A. Stefanov and J.L.

O’Brien. In Nature Photonics, 3:346, 2009.[5] A. Laing, et al. arXiv:1004.0326v2, 2010.[6] A. Politi, J. C. F. Matthews and J.L. O’Brien. In Science,

325:1221, 2009.[7] J. C. F. Matthews, A. Politi, D. Bonneau, and J. L.

OBrien. arXiv:1005.5119 , 2010.[8] A. Peruzzo, et al. Submitted.[9] J. P. Hadden, et al. arXiv:1006.2093 (2010).

[10] C Natarajan, et al. In APL, 96:211101 (2010)

Generation of objective randomness via realistic optical statesDenis Sych and Gerd Leuchs

Max Planck Institute for the Science of Light, Günther-Scharowsky-Strasse 1 / Bau24, 91058 Erlangen, Germany

Institute for Optics, Information and Photonics; University of Erlangen-Nuremberg, Staudtstrasse 7 / B2, 91058 Erlangen, Germany

denis.sych@mpl.mpg.de

The problem of generation random numbers with help of optical quantum measurements is considered. We demonstrate how to generate numbers which are 1) completely random in statistical sense, i.e. they have no regular statistical patters, 2) provably secure, i.e. a priori unknown for any potential eavesdropper, and 3) asymptotically unique, i.e. an infinitely long sequence of these numbers can be obtained in only one copy. A working experimental realization based on homodyne detection of the vacuum state is shown to comply with the above three conditions.

Generation of random numbers is an important task in many areas ranging from fundamental science to particular applications. Depending on a given situation, a random sequence can be defined in many ways which would reflect the required properties. Probably the most essential and commonly used feature of random number generators (RNG) is to produce irregular sequences of numbers with sufficiently good statistical properties such as high value of entropy, absence of self-correlations or periodicity, etc. Thus a usual way to test randomness of a sequence is to run it through various computer tests, which try to reveal the possible mathematical patterns. The easiest and cheapest way to produce statistically random sequences is to use software RNG, based on various mathematic algorithms. Modern software RNG can be relatively fast and are able to produce highly stochastic sequences. An unavoidable feature of these RNG is that they are inherently deterministic, i.e. sequences of numbers produced by this type of RNG are pre-defined, and all copies of the same RNG produce the same sequences. In a sense, the pre-defined random sequence can be called subjectively random, as its randomness is a matter of subjective knowledge, e.g. knowledge of a specific algorithm which generates it. The sequence looks random only due to the lack of this knowledge.

A more stringent condition is to produce aperiodic indeterministic random sequences. Clearly, such sequences cannot be obtained with help of mathematical algorithms only, but should rely on physical mechanisms. For instance, chaotic systems in classical dynamics can demonstrate rather unpredictable behavior, which lies at the basis of many classical hardware RNG. The best implementations of chaotic RNG can be very fast, whilst providing data with high percentage of passing the statistical tests. Nevertheless, chaotic dynamics in principle can contain somewhat hidden patterns, which are still a subject for research. Strictly speaking, the origin of this type of randomness is hard to characterize and prove. Even if the possible patterns are not recognized by modern statistical tests, nothing prevents this possibility in future. Thus this type of sequences can be also classified as subjectively random.

As an ultimate case, one can ask for a random sequence which is not only statistically random and indeterministic, but also physically unpredictable, i.e. uncorrelated with any other physical system except the system that generates it [1]. We will call this type of randomness as objective randomness, to make contrast with previously discussed subjective randomness. By definition, the origin of objectively random sequences is not a matter of lack of knowledge, but is an objective property. We note, that such definition can be considered as a generalization of algorithmic randomness, as the latter one considers predictability by a specific type of systems, namely by classical Turing machine. In the case of objective randomness, we do not specify what kind of physical system should be used to search for potential predictability: it can be classical or quantum computer, as well as any other physical system that objectively exists. As a result of such generalization, objectively random sequence is also perfectly random in statistical sense.

In this talk, we discuss the problem of generation such objectively random sequences. As it has been shown recently, the fluctuations of homodyne measurement results of the minimum energy pure vacuum state satisfy the conditions of objective RNG [2]. We demonstrate how to eliminate the influence of experimental imperfections and uncontrollable classical noise and guarantee that the resulting sequence is objectively random. As a further extension, we derive the minimum amount of objective randomness which can be obtained by measuring any realistic mixed state in a given noisy measurement.

[1] D. Sych and G. Leuchs, “Quantum uniqueness”, arXiv:1003.1402 (2010)[2] Ch. Gabriel, Ch. Wittmann, D. Sych, R. Dong, W. Mauerer, U. Andersen, Ch. Marquardt, and G. Leuchs, “A Generator for Unique Quantum Random Numbers Based on Vacuum States”, accepted to Nature Photonics (2010)

Correlations in phase space and the creation of focusing wave packets Wolfgang P. Schleich, Institut für Quantenphysik Albert-Einstein-Allee 11 D-89081 Ulm Correlations are at the very heart of quantum mechanics. In the familiar Einstein–Podolsky–Rosen situation [1] entangled particles can display correlations that are stronger [2] than their classical counterparts. These correlations act in phase space [3] and can manifest themselves in the phenomenon of focusing wave packets [4], even in the absence of any classical force. This focusing effect takes place under very limited circumstances and depends crucially on the number of dimensions. Indeed, it appears exclusively in one [5] and two dimensions. In the present paper we study [6] this phenomenon in one space dimension, derive a condition for its occurrence and optimize the effect [7]. References [1] A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777–780 (1935). [2] J.B. Bell, Physics 1, 194 (1964). [3] J.P. Dahl, R. Mack, A. Wolf, and W.P. Schleich, Phys. Rev. A 74, 042323 (2006). [4] I. Bialynicki-Birula, M.A. Cirone, J.P. Dahl, M. Fedorov, and W.P. Schleich, Phys. Rev. Lett. 89, 060404 (2002). [5] V.V. Dodonov, and M.A. Andreata, Phys. Lett. A 310, 101–109 (2003). [6] R. Mack, V.P. Yakovlev, and W.P. Schleich, J. Mod. Opt. 57, 1437-1444 (2010). [7] K. Vogel, F. Gleisberg, N.L. Harshman, P. Kazemi, R. Mack, L. Plimak, and W.P. Schleich, Chemical Physics, to appear in October 2010.

Electromagnetically Induced Transparency in Mechanical Effects of Light

G S AgarwalDepartment of Physics, Oklahoma State University, Stillwater, OK 74078

The current research in nano mechanical systems is driven by the possibility of

1

realizing the quantized motion of macroscopic systems. Efforts are on to cool such systems to their ground state so that quantum optical effects can be realized.In the meanwhile the nonlinear optical studies of such systems is yielding remarkable results. We have rather surprisingly found the possibility of EIT in such systems opening up the possibility of applying all that one has learnt about EIT in last two decades. We discuss the EIT in both dispersively and reactively coupled nano mechanical systems. We also discuss quadratically coupled systems where EIT arises from thermal fluctuations.

State and process reconstruction using Kalman filtering -- a diagnostic

tool for quantum engineering

Stefan Scheel

Imperial College Successful quantum engineering of light and matter relies to a large extent on one's ability to generate and coherently manipulate a desired quantum state. Quantum tomography provides a tool to assess the quality of the quantum states and processes involved. I will present a novel quantum tomographic reconstruction method based on Bayesian inference via the Kalman filter update equations. This methods not only yields the optimal Bayesian reconstruction, but in addition provides error bars on any derived quantity. I will describe the basic principle behind Kalman filter based reconstruction for perfect and imperfect photodetections. This is a first step towards the broader goal of devising an omnibus reconstruction method that could be adapted to any tomographic setup and that treats measurement uncertainties in a statistically well-founded way.

Two two-level atoms in a cavity: Entanglement versus Decoherence and Dirac

oscillators.

Thomas Seliman We show hat two different two-level atoms coupled to the same mode of a cavity and interacting with an Ising and a Dipole-Dipole interaction has two invariants and can be solved in closed form. This model embodies several well- known cases sovability and serves in an ideal way to test the behaviour of entanglement between the two modes and the loss of coherence by entanglement with the cavity. With the wide range of parameters we can get a variety of behaviours, some of which we shall display in C-P plots. In particular this system allows to mimic one- and two-dimensional Dirac-Moshinsky oscillators including the coupling to am isopsin field. We hope to convince some experimentalists, that it is worth while to perform such toy-experiments, which involve exactly solvable relativistic three degrees of freedom systems.

Quantum Images from Four-Wave Mixing in Rb Vapor Paul D. Lett National Institute of Standards and Technology and Joint Quantum Institute, NIST/Univ. of Maryland 100 Bureau Drive Gaithersburg, MD 20899 USA Abstract: Until recently, parametric downconversion in optical crystals was the only way in which multi-spatial-mode squeezed light was generated. With such crystals one can obtain cones of correlated spontaneously-emitted photons, but it generally requires large pump powers and thus pulsed sources. In addition, phase matching constraints in the nonlinear crystals are rather severe. This makes it difficult to generate quantum correlations simultaneously across the large range of angles or spatial frequencies required to form a detailed image with a single frequency of light. Recently, inspired by related work at the single-photon level by a number of groups, we developed a 4WM scheme that enables one to generate strong levels of squeezing in bright beams using rather simple technology [1]. This scheme uses an off-resonant double-lambda energy level configuration in Rb atoms in a hot vapor cell. The scheme requires relatively undemanding technology and generates strongly squeezed light near the Rb atomic resonance that can thus readily be coupled to available atomic memories and qubits for quantum information operations. The source has the additional and important feature that twin-beam squeezed light in multiple spatial modes can be easily generated, and thus images can be produced that contain strong quantum correlations. The twin beams are highly correlated in both their intensity and phase. Using this source we have generated multi-spatial-mode images that are entangled at a level that displays the Einstein-Podolsky-Rosen paradox [2]. The images can be composed of bright fields that display position-dependent quantum noise reduction in their intensity difference, or vacuum twin beams that are strongly entangled when projected onto a large range of different local oscillator spatial modes. The system is a good source for use in parallel continuous-variable quantum information protocols as well as quantum imaging applications. 1. McCormick, C.F., V. Boyer, E. Arimondo and P.D. Lett, "Strong relative intensity squeezing by 4-wave mixing in Rb vapor," Opt. Lett., 32, 178 (2007). 2. Boyer, V., A. Marino, R. Pooser and P. Lett, "Entangled images from four-wave mixing," Science, 321, 544 (2008).

Multiphototon transitions in cavity QED assisted by a strong external field.

N. Zagury and P. Milman

Instituto de Física, Universidade Federal do Rio de Janeiro, R. J. , Brazil

e-mail: zagury@if.ufrj.br Abstract: We consider a two-level atom inside a cavity driving by a strong external field. The transition probabilities involving the exchange of two three and four photons of the cavity are calculated using an unitary expansion for the time evolution operator and obtaining an effective hamiltonian for each order of transition. Possible applications are discussed.

Quantum Optics V, Cozumel, Mexico: Nov. 15-19, 2010

Pauli graphs when the Hilbert space dimension contains asquare: why the Dedekind psi function?

by Michel Planat

Institut FEMTO-ST, 32 Avenue de l’Observatoire, 25044Besancon Cedex (France) michel.planat@femto-st.fr

(oral presentation asked)

We study the commutation relations within the Pauli groups builton all decompositions of a given Hilbert space dimension q, contain-ing a square, into its factors. Illustrative low dimensional examplesare the quartit (q = 4) and two-qubit (q = 22) systems, the octit(q = 8), qubit/quartit (q = 2× 4) and three-qubit (q = 23) systems,and so on.

In the single qudit case, e.g. q = 4, 8, 12, . . ., one defines a bi-jection between the σ(q) maximal commuting sets [σ[q) the sum ofdivisors of q] of Pauli observables and the maximal submodules ofthe modular lattice Z2

q, that arrange into the projective line P1(Zq)and a independant set of size σ(q) − ψ(q) [with ψ(q) the Dedekindpsi function].

In the multiple qudit case, e.g. q = 22, 23, 32, . . ., the Pauli graphsrely on symplectic polar spaces such as the generalized quadranglesGQ(2, 2) (if q = 22) and GQ(3, 3) (if q = 32). More precisely, inthe dimension pn (p a prime) of the Hilbert space, the observablesof the Pauli group (modulo the center) are seen as the elements ofthe 2n-dimensional vector space over the field Fp and one makes useof the commutator to define a symplectic polar space W2n−1(p) ofcardinality σ(p2n−1), that encodes the maximal commuting sets ofthe Pauli group by its totally isotropic subspaces. Building blocks ofW2n−1(p) are punctured polar spaces (i.e. a observable and all max-imum cliques passing to it are removed) of cardinality the Dedekindpsi function ψ(p2n−1).

For multiple qudit mixtures (e.g. qubit/quartit, qubit/octit andso on), one finds multiple copies of polar spaces, ponctured polarspaces, hypercube geometries and other intricate structures. Suchstructures play a ubiquitous role in the quantum information science.

1

Experimental realisation of sub shot noise quantum imaging Giorgio Brida, Marco Genovese, Alice Meda, Ivano Ruo Berchera

Quantum properties of the optical field represent a resource of the utmost relevance for the development of quantum technologies, allowing unprecedented results in disciplines ranging from quantum information and metrology to quantum imaging. A very interesting example is offered by the possibility of sub shot noise measurements with quantum optical states In particular a very interesting achievement would derive from the detection of weak objects by exploiting the quantum correlations of parametric down conversion (PDC) emission: a result that could have important practical applications. A little more in detail the principle of this technique is to take advantage of the correlation in the noise of two conjugated branches of PDC emission : in fact, subtracting the noise measured on one branch from the image of a weak object obtained in the other branch, the image of the object, eventually previously hidden in the noise, could be restored [1]. In this talk we will show how we have reached a sub shot noise [2] regime and then improved this result up to reach a regime where it was possible to achieve the first experimental realisation of sub shot noise imaging [3]. [1] Brambilla, E., Caspani, L., Jedrkiewicz, O., Lugiato, L. A. & Gatti, A. Phys. Rev. A 77, 053807 (2008). [2] G. Brida et al., Phys. Rev. Lett. 102, 213602 (2009). [3] G.Brida, M. Genovese, I. Ruo Berchera, Nature Photonics 4, 227 - 230 (2010). G.Brida, M. Genovese, A.Meda, I. Ruo Berchera, arXiv1005.366553

Towards a complete characterization of the polarization of quantum states

A. B. Klimov,1 G. Bjork,2 J. Soderholm,2, 3, 4 U. L. Andersen,5 Ch. Marquardt,3, 4 G. Leuchs,3, 4 and L. L. Sanchez-Soto3, 4

1Departamento de Fısica, Universidad de Guadalajara, 44420 Guadalajara, Jalisco, Mexico2School of Communication and Information Technology,

Royal Institute of Technology (KTH), Electrum 229, SE-164 40 Kista, Sweden3Max-Planck-Institut fur die Physik des Lichts, Gunther-Scharowsky-Straße 1, Bau 24, 91058 Erlangen, Germany

4Universitat Erlangen-Nurnberg, Staudtstraße 7/B2, 91058 Erlangen, Germany5Department of Physics, Technical University of Denmark, Building 309, 2800 Kongens Lyngby, Denmark

(Dated: October 4, 2010)

We propose a complete hierarchy of operational degrees of polarization in terms of the moments of the Stokesvector. We first examine the properties of the second-order definition and carry out its experimental determina-tion. Quantum states with the same standard (first-order) degree of polarization are correctly discriminated bythis new measure. We suggest the construction of the higher-order degrees.

Quantum entanglement in warm baths

Gershon Kurizki Weizmann Institute , Rehovot 76100 , Israel

I will review our recent findings that defy the common notion that entanglement in multipartite systems does not survive in thermal environments. The truth is that both harmonic oscillators and multispin (multiatom ) systems may become entangled because of the bath to which they couple .Spin ensembles acting as a bath are much less conducive to such entanglement. The most distinct form of such entanglement is that of Schroedinger- cat states ( or macroscopic quantum- superposition states ), which are synonimous with GHZ states in multispin systems. Other entangled states obtain whenever the coupling to the bath varies from one spin ( or oscillator ) to another. Dynamic control aimed at preserving these states will also be discussed . Experimental realizations will be focused on.

Nonclassicality made visible

W. Vogel, T. Kiesel, and J. Sperling

Arbeitsgruppe Quantenoptik, Institut fur Physik,

Universitat Rostock, D-18051 Rostock, Germany

Abstract – The notion of nonclassicality in quantum optics is usually based on the failure

of the Glauber-Sudarshan P function to be interpreted as a classical probability distribution.

Since the P function can be strongly singular, it is in general hard to visualize this property

in experiments. Here we show how one can regularize the P function [1], which leads us to

the concept of nonclassicality quasi-probabilities. These distributions are regular functions

in general, the nonclassicality is reflected by their negativities. The proposed method is

rather simple and it applies to any quantum state. Moreover, it works for the noisy data as

they are obtained in experiments, which is illustrated for some examples.

Presently a special nonclassical property receives a lot of attention: the quantum entan-

glement. It is considered to be a key resource for various applications in quantum technology.

To directly visualize entanglement, we introduce entanglement quasi-probabilities [2]. Since

the representation of entangled quantum states via pseudo-mixtures of pure separable states

is ambiguous, this requires an optimization procedure. This leads also to regular distribu-

tions, which show negativities if the state is entangled. Whenever a state is separable, the

entanglement quasi-probability has the property of a classical probability. This method is

valid in general, including mixed continuous-variable quantum states.

[1] T. Kiesel and W. Vogel, Nonclassicality filters and quasi-probabilities, Phys. Rev. A 82, 032107

(2010).

[2] J. Sperling and W. Vogel, Representation of entanglement by negative quasiprobabilities, Phys.

Rev. A 79, 042337 (2009).

Light squeezing by single passage through an atomic sample

Arturo Lezama Instituto de Física, Universidad de la República, C. Postal 30, 11000, Montevideo,

Uruguay

The long living coherence among ground state atomic sublevels, has been identified as a convenient medium for the storage and processing of quantum states of light [1]. Such effects require the availability of non-classically prepared light beams with frequencies corresponding to resonant atomic transitions. Quadrature squeezed light at the D1 or D2 transitions of alkali atoms is difficult to obtain using the standard procedure of parametric down conversion in non-linear crystals [2]. In this talk I review the present status of ongoing research seeking the generation of squeezed vacuum through single passage of a light beam across an atomic sample.

Light squeezing by resonant interaction with an atomic transition has been predicted as a manifestation of the nonlinear optical effect of polarization self-rotation (PSR) [3]. Substantial amounts of squeezing, up to 6 dB, were foreseen. However, actual experiments [4-7] have achieved significantly smaller values of squeezing (< 1.4 dB) while the squeezing occurs for a limited range of experimental parameters and shows interesting spectral structures.

In order to understand such results, we have developed a theoretical model [8] of the light atom interaction taking into account the full Zeeman and hyperfine structure of the corresponding transitions. Such model reveals the important role played played by serveral mechanisms such as transit time, optical pumping, FWM and Stark shifts. Comparison with the experimental results obtained in room temperature atomic vapor samples is presented. A simplified picture of the squeezing mechanism is introduced. Finally, the possibility of light squeezing in cold atomic samples is discussed. [1] L.-M. Duan, M. D. Lukin, J. I. Cirac and P. Zoller, Nature, 414, 413 (2001). [2] G. Hétet, O. Glöckl, K. A. Pilypas, C. C. Harb, B. C. Buchler, H.-A. Bachor, and P. K. Lam. Journal of Physics B, 40, 221-226 (2007). [3] A. B. Matsko, I. Novikova, G. R.Welch, D. Budker, D. F. Kimball, and S. M. Rochester. Phys. Rev. A, 66, 043815 (2002). [4] J. Ries, B. Brezger, and A. I. Lvovsky. Physical Review A, 68, 025801 (2003). [5] Eugeniy E. Mikhailov and Irina Novikova. Opt. Lett., 33, 1213 (2008). [6] Eugeniy E. Mikhailov, Arturo Lezama, Thomas W. Noel, and Irina Novikova. JMO, 56, 1985 (2009). [7] Imad H. Agha, Ga_etan Messin, and Philippe Grangier. Opt. Express, 18, 4198 (2010). [8] A. Lezama, P. Valente, H. Failache, M. Martinelli, and P. Nussenzveig. Phys. Rev. A 77, 013806 (2008).

An statistical approach to the entanglement decay of two-qubit systems

K. M. Fonseca Romero, J. R. Martínez, C. Viviescas

Universidad Nacional de Colombia, Departamento de Física, Cra. 30 No. 45-3 Edificio 405 Oficina 207, Bogotá, Colombia

kmfonsecar@unal.edu.co

The study of entanglement decay is fundamental to assess the resilience of quantum information processes. It has been found that entanglement, in contrast to coherences --which decay asymptotically--, can decay in finite time: a phenomenon known as entanglement sudden death. We investigate not only how typical is this phenomenon, but also if it can be used to characterize entanglement decay. We study the evolution of concurrence of the whole set of two-qubit pure states, uniformly distributed, assuming independent identical reservoirs for the qubits, and find that entanglement sudden death can be or not typical. We calculate the probability distributions of concurrence and of the disentanglement times, and show that the latter turns out to be insufficient to assess if entanglement can be used in quantum information processing.

Non-equlibrium thermal entanglement for simple qubit systems

Ilya Sinayskiy,∗ Nathan Pumulo, and Francesco Petruccione†Quantum Research Group, School of Physics and National Institute for Theoretical Physics,

University of KwaZulu-Natal, Durban, 4001, South Africa

In describing real physical systems one should always take into account the influence of the surroundings. Thestudy of open systems is particularly important for understanding processes in quantum physics [1].

Here we consider a chain of qubits, consisting of two and three qubits. The first and the last qubit are coupled toseparate bosonic baths at different temperatures. The total Hamiltonian of the system is given by

H = HS + HB1 + HBN + HSB1 + HSBN , (1)

where HS is the Hamiltonian of the qubit subsystem,

HS =N∑

i=1

εi

2σz

i + K

N−1∑

i=1

(σ+

i σ−i+1 + σ−i σ+i+1

), (N = 2, 3) . (2)

The Hamiltonians of the reservoirs for the first qubit (j = 1) and the last qubit (j = N) are given by

HBj =∑

n

ωn,j b†n,j bn,j . (3)

The interaction between the qubit subsystem and the bosonic baths is described by

HSBj = σ+j

∑n

g(j)n bn,j + σ−j

∑n

g(j)∗n b†n,j , (4)

of course σ±j , σzj are the well-known Pauli matrices and b†n,j , bn,j denote bosonic creation and annihilation operators.

In Born-Markov approximation the equation for the evolution of the reduced density matrix ρ of the qubit subsystemis [1–3]:

dρ

dt= −i[HS , ρ] + L1(ρ) + LN (ρ) (5)

with dissipators

Lj(ρ) ≡∑µ,ν

J (j)µ,ν(ωj,ν){[Vj,µ, [V †

j,ν , ρ]]− (1− eβjωj,ν )[Vj,µ, V †j,ν ρ]}. (6)

The operators Vj,µ are responsible for transitions in the system under the action of the reservoirs.In the both cases, two [2] and three qubits [4], we found an analytical expression for the reduced density matrix

of the qubit subsystem. We studied the dynamics of the system and showed its convergence to a steady state. Weanalyzed the dynamics of entanglement and performed a comparison of the steady state concurrence of two and threequbit chains.

[1] H.-P.Breuer and F.Petruccione, The Theory of Open Quantum Systems (Oxford University Press, 2002)[2] I. Sinaysky, F. Petruccione and D. Burgarth, Phys. Rev. A, 78, 062301 (2008).[3] A. Sergi, I. Sinayskiy and F. Petruccione, Phys. Rev. A, 80, 012108, (2009).[4] N. Pumulo, I. Sinayskiy, F. Petruccione, (submited)

∗Electronic address: sinayskiy@ukzn.ac.za†Electronic address: petruccione@ukzn.ac.za

CORRELATED PHOTON PAIRS FROM FOUR-WAVE MIXING IN RUBIDIUM VAPOR.

Francisco E. Becerra1,2

, Richard T. Willis2

, Steven L. Rolston2

, Luis A. Orozco2

, CINVESTAV,

Mexico1

, Joint Quantum Institute, Department of Physics, University of Maryland and National

Institute of Standards and Technology2

Contact Author: Francisco E. Becerra, Joint Quantum Institute, Department of Physics, University of Maryland National Institute of Standards and Technology, College Park, Maryland 20742, USA, fbecerra@umd.edu

Introduction

The process of Four-Wave Mixing (FWM) generates correlations and entanglement due to the

requirements of conservation of energy, momentum, and angular momentum. This process can

produce light at specific frequencies not available with direct electromagnetic sources. The non-

degenerate diamond configuration of the energy levels of rubidium, one ground state 5S1/2; two

excited states 5P1/2 and 5P3/2; and one double exited state 6S1/2 allows the generation of light at

telecommunication wavelengths. We study the generation of correlated photon pairs from

spontaneous FWM, one photon at 1.3 μm (telecommunication wavelength) and another at 780

nm, resonant with an atomic transition in rubidium.

Experiment

We use warm rubidium vapor contained in a glass cell (≈100 ºC) to generate correlated pairs of

photons from a spontaneous FWM process after a two-photon excitation with two strong pumps

on two-photon resonance in rubidium. The non-degenerate energy-level configuration used

allows us to spatially separate the generated photon pairs from the strong pump light. The pairs

of photons generated in this way show correlations in propagation direction, frequency, time and

polarization.

We study the temporal correlations and spectral properties of the photon pairs, which can be

modified by the frequency detunings of the two pump lasers involved in the process. We observe

quantum interference between different decay paths of the FWM process, and we use the

frequencies of the pumps to select specific decay paths in the energy level structure. The pairs of

photons show entanglement in polarization characterized by strong violations of Bell's

Inequalities.

Work Supported by NSF and CONACYT.

Improving Quantum Key Distribution Systems by Quantum Hacking Tests Carlos Wiechers, 1, 2, 3, Lars Lydersen, 4, 5, Nitin Jain, 1, 2, Christoffer Wittmann, 1, 2, Dominique Elser, 1, 2,, Vadim Makarov, 4 Christoph Marquardt, 1, 2, José L. Lucio, 3 Johannes Skaar, 4, 5 and

Gerd Leuchs 1, 2 1) Max Planck Institute for the Science of Light, Günther-Scharowsky-Str. 1/Bau 24, 91058 Erlangen, Germany 2) Institut für Optik, Information und Photonik, University of Erlangen-Nuremberg, Staudtstraße 7/B2, 91058, Erlangen, Germany 3) Departamento de Física, Campus León, Universidad de Guanajuato, Lomas del Bosque 103, Fraccionamiento Lomas del Campestre, 37150, León, Guanajuato, México 4) Department of Electronics and Telecommunications, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway 5) University Graduate Center, NO-2027 Kjeller, Norway

Abstract Quantum key distribution [1] has evolved rapidly in the last decades. Today, QKD implementations in laboratories can generate key over fiber channels with lengths of 250 km [2] and QKD systems are even commercially available [3] promising provably enhanced security in communication. However, experimental realizations of QKD always deviate in some aspects from the theoretical models of the security proofs. This has led to iterations where security threats caused by deviations have been discovered, and the loopholes have been closed either by modification of the implementation, or by more general security proofs [4–5]. In this work, we present three methods to exploit loopholes in commercial QKD systems. The first two loop-holes are due to deviations of single photon detectors (InGaAs/InP) from the ideal behavior, when operated outside the gated mode [7]. Furthermore, we manipulate the time-dependent efficiency of two single photon detectors such that an eavesdropper can gain information by time-shifting signal pulses [8]. The eavesdropper can exploit these loopholes in an intercept-resend attack thus obtaining the same raw data as the legitimate receiver. We also propose general as well as particular solutions to close the discovered loopholes. Openly discovering and closing security loopholes is an important step to strengthen practical secure QKD. Keywords: Quantum Key Distribution, Quantum Hacking, Loopholes. [1] V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dŭsek, N. Lütkenhaus, and M. Peev, Rev. Mod. Phys.,

81, 1301 (2009).

[2] D. Stucki et al., New J. Phys., 11, 075003 (2009).

[3] Commercial QKD systems are available from at least three companies: ID Quantique (Switzerland), http://www.idquantique.com; MagiQ Technologies (USA), http://www.magiqtech.com; SmartQuantum (France), http://www.smartquantum.com.

[4] D. Gottesman, H.-K. Lo, N. Lütkenhaus, and J. Preskill, Quant. Inf. Comp., 4, 325 (2004).

[5] C.-H. F. Fung, K. Tamaki, B. Qi, H.-K. Lo, and X. Ma, Quant. Inf. Comp., 9, 131 (2009).

[6] L. Lydersen and J. Skaar, Quant. Inf. Comp., 10, 0060 (2010).

[7] L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, to appear in Nat. Photonics; C. Wiechers, L. Lydersen, C. Wittmann, D. Elser, C. Marquardt, J. Skaar, G. Leuchs, and V. Makarov, in preparation.

[8] V. Makarov, A. Anisimov, and J. Skaar, Phys. Rev. A, 74, 022313 (2006), erratum ibid. 78, 019905 (2008); Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.- K. Lo, Phys. Rev. A, 78, 042333 (2008).

Elements of a photonic quantum network

Ian A. Walmsley, Hendrik Coldenstrot-Ronge, Klaus Reim, Nick Thomas-Peter, Michael Hu,Tim Bartley, Josh Nunn, Lijian Zhang,

Nathan Langford and Brian J. Smith Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU,

UK walmsley@physics.ox.ac.uk

Photonics provides a promising route to implementing quantum-enhanced technologies. Underpinning this technology lies the generation, manipulation and stabilization of multi-photon entangled states. Waveguide structures provide important physical features that enable these, as well as convenient structures for scaling to larger numbers of photons. Quantum technologies promise to enhance the capabilities of transmission and processing of information beyond what is possible using classical physics. Applications are envisaged to communications, cryptography, metrology, imaging and computation. All-optical versions of these technologies exist in principle, based on uniquely quantum features such as reduced noise, increased correlations and measurement back-action that are fundamentally different that those used in the design of classical optical analogues of these processing devices.

The distribution of photonic entangled quantum states and their application to real-world processing tasks is therefore a central element of quantum information science. In order to realize quantum gains, such states and protocols must operate beyond the classical limits even in the presence of noise, including especially photon loss. The key capabilities that enable this technology are the preparation of appropriate photonic quantum states,[1,2] the manipulation of these in response to external controls,[3] the storage of the outputs of the processing [4] and the measurement of these outcomes.[5] The design of such systems must account for the imperfections of real implementations,[6] and for the feasibility of the construction of the input states and output measurements.

We shall describe recent work in the synthesis and application of entanglement to loss-tolerant communications and metrology. In particular, this will include the development of waveguide-based devices, and the design of optimal protocols for inefficient quantum detector and lossy channel estimation, and for entanglement distillation.

Integrated optics contributes key enabling technology for these purposes. The key features of waveguides that are critical for such development include control of dispersion by means of the guide size, controllable birefringence, stability of multiple-nested interferometers, flexibility of detection, and stronger photon-matter interaction.

References [1] O. Cohen et al. Phys. Rev. Lett. 102, 123603 (2009) [2] B. J. Smith et al., Opt. Exp., 17, 23589-23602 (2009) [3] B. J. Smith et al., Opt. Express 17,13516 (2009) [4] G. Puentes et al., Phys. Rev. Lett., 102, 080404 (2009) [5] K. Reim et al., Nat. Phot., 4, 218 (2010) [6] M. Kacprowicz, et al., Nat. Phot., 4, 357 (2010)

Dynamics of quantum systems forming interacting networks

J. Novotný1,2, G. Alber1, I. Jex2

1) Institut für Angewandte Physik, TU-Darmstadt, Schlosstrasse 4a, D-64289 Darmstadt, FRG

2) Department of Physics, FJFI ČVUT v Praze, Břehová 7, 115 19 Praha 1, Czech Republic

Networks - arrangements of simple physical object represent an exceptionally universal tool in physics. Classical physics uses network at a large scale. It is particularly useful to model rather complicated ranging from interacting atoms in lattices to the dynamics of members of a social community. In all the cases the models are used to explain basic features of the system rooted in the elementary interactions which manifest themselves as the macroscopiuc properties of the system. The study of analogous models in quantum mechanics might seem straigtforward but the contrary is the case. The quest to solve the quantum dynamics of networks faces certain serious difficulties eventhough the dynamics can be simple [1,2]. Quantum networks can have different degree of complexity. In the simplest case we can imagine the individual elements to be two-level systems (qubits) with a simple form of interaction between them. We will consider the interaction between the qubits being random and that it can be given as an iterative procedure. At each instant one unitary quantum operation (representing the interaction between quantum systems) will be applied. The analytic treatment of such systems is not easy. One of the reasons is numerical. The space of the system grows exponentially with the number of qubits. The detailed time evolution of the system becomes almost impossible to solve already for a moderate number of qubits. However, when we limit ourselves to studies of the long time (asymptotics) dynamics it becomes possible to obtain very specific and even analytic answers with a rather broad validity range [3,4]. We present results on studies of ensembles of qubits with interactions simulated by unitary transforms. Mathematically these models fall under the notion of random unitary channels. We show that the long time dynamics of such systems can be given exclusively by so called attractors formed by eigenvectors of the random unitary channels corresponding to eigenvalues of amplitude one. We show how to obtain the relevant eigenstates. They are determined by generalized commutation relations involving Kraus operators defining the random unitary channel. After analyzing the general analytic form of the asymptotic dynamics we discuss the implications for a network involving controlled unitary operations as the interaction between qubits. Interesting links to graph theory and qauntum communication are pointed out. [1] A. S. Holevo, Statistical Structure of Quantum Theory, Springer, Berlin, (2001). [2] D.W. Kribs, Proceedings of the Edinburgh Mathematical Society 46, 421 (2003). [3] J. Novotny, G. Alber, I. Jex, J. Phys. A 47, (2009) [4] J. Novotny, G. Alber, I. Jex , Asymptotic Evolution of Random Unitary Operations, arXiv:0908.4534

Minimal Tomography and Coincidence Maps for characterizing two and four photonic spatial qubits

S. Pádua

Departamento de Física, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970, Belo Horizonte-Brasil. Photonic path states produced when photon pairs generated by parametric down-conversion cross double or multiple slits allowed us to study the generation of high dimension qudits states [1], measurement of its photonic path state entanglement [2] and its characterization[3]. We show in this seminar two more recent quantum information experiments where photon pairs in path states and a spatial light modulator are employed for doing minimum tomography in their state. In a second experiment, photonic four qubits path states are generated and characterized. Four photons or two-pairs are generated when a pulsed pump beam cross a type II PPKTP crystal. The four qubits path states are generated when the two-photon pairs cross a double-slit.

Quantum state tomography is a technique where any state of a quantum system can be completely characterized using an ensemble of many identical particles [1]. A sequence of measurements within a series of different bases allows the reconstruction of the density matrix that represents the system state. In the standard six-state tomography of qubits three orthogonal components of the qubit analog of Pauli's spin vector operator are measured, so that six probabilities are estimated for determination of three real parametes that specify the qubit state [4]. Rehacek, Englert and Kaszlikowski developed a symmetric and efficient scheme for the determination of the density matrix of a qubit where only four measured probabilities are enough [5]. In the four state tomography scheme, four non-coplanar vectors define four measurements operators that govern the detector readings and form a set of complete POVMs [3]. These four vectors form a tetrahedron in the Poincare sphere, and the states defined by the vectors in the sphere are used for building the four POVMs used in the state estimation. In reference [6], the authors have used the four measurements scheme for measuring the one photon polarization state and the extended sixteen-state scheme for measure the photon pair entangled state in polarization variables. We have applied the minimum measurement tomography scheme proposed in reference [5] for obtaining the density matrix of two qubits state in spatial variables. Photon pairs are generated by spontaneous parametric down-conversion and the two-qubit states in spatial variables are generated by letting the photon pair to cross two double-slits, respectively. The POVMs are produced by using polarizers and a spatial light modulator (SLM) that reflects the light transmitted by the double-slits and introduces amplitude and phase variations in the photon paths. Sixteen measurements for the two-qubits states allow the estimation of the density operators representing the system state.

Control of spatial quantum correlations in biphotons is one of the fundamental principles of Quantum Imaging. Up to now, experiments have been restricted to controlling the state of a single biphoton, by using linear optical elements. We demonstrated experimentally the control of the spatial quantum correlations in a four-photon state comprised of two pairs of photons. Our scheme is based on a high-efficiency parametric down-conversion source coupled to a double slit by a variable linear optical setup, in order to obtain spatially encoded qubits. Both entangled and separable pairs have been obtained, by altering experimental parameters. We show how the correlations influence both the interference and diffraction on the double slit . Measurements for determining the generated states require us to go to the diagonal basis of the path states. For qubits encoded on transverse spatial variables, this can be achieved by looking at coincidence measurements on the pattern generated in the far field of the slits. One way to access the far field is to use a lens with focal length f in the f − f configuration. This maps the Fourier transform of the slits onto positions on the detection plane. We show how the Coincidence maps measured with photons of the two-pairs with the same polarization and with ortohogonal polarization alowed us to characterize the four qubits path states.

[1]L. Neves, G. Lima, J. G. Aguirre, C. H. Monken, C. Saavedra, and S. Pádua, Phys. Rev. Lett. 94, 100501 (2005), G. Lima, L. Neves, I. F. Santos, J. G. Aguirre, C. Saavedra, and S. Pádua, PHYS. REV. A 73, 032340 (2006).

[2]L. Neves, G. Lima, E. J. S. Fonseca, L. Davidovich, S. Pádua, Phys. Rev. A 76, 032314 (2007).

[3]G. Lima, F. A. Torres-Ruiz, L. Neves, A. Delgado, C. Saavedra and S. Pádua, J. Phys. B.: At. Mol. Opt. Phys. 41, 185501(2008),

[4] J. B. Altepeter, E. R. Jeffrey, and P. G. Kwiat, “Chap. 3: Photonic State Tomography,” Advances in AMO Physics, Vol. 52 (Elsevier, 2006).

[5] J. Rehácek,B.-G.Englert, and D. Kaszlikowski, Phys. Rev. A 70, 052321 (2004).

[6]A. Ling, K. P. Soh, A. Lamas-Linares, and C. Kurtsiefer, Phys, Rev. A 74, 022309 (2006).

Photonic quantum-state manipulation by single-photon operations Myungshik Kim QOLS, Imperial College London, SW7 2BW, United Kingdom We have witnessed a prolific growth in theoretical and experimental efforts to understand and control physical systems in a quantum level. In particular, possibilities to apply quantum mechanics towards the radical improvement of information technology have attracted attention from various branches of physics and beyond. Ever since the advent of lasers, optics has been closely related to the foundations and applications of quantum physics because of its controllability to a very fine level. However, photons do not interact with each other, which makes it difficult to engineer their states. In order to overcome this problem, various schemes have been suggested. In a quantum optics laboratory, Gaussian states, whose phase properties are described by Gaussian probability-like functions, have been generated but there is some limitation in using them for various tasks of quantum information processing. There have been suggestions and realizations to engineer the quantum state by single-photon level operations including photon addition, subtraction and scissors operations. In this talk, we show how to realize single-photon level operations and how they are used to manipulate the quantum states of travelling fields. [1] M. S. Kim, J. Phys. B 41, 133001 (2008) [2] M. S. Kim, H. Jeong, A. Zavatta, V. Parigi and M. Bellini, Phys. Rev. Lett. 101, 260401 (2008) [3] S. C. Springer, J. Lee, M. Bellini and M. S. Kim, Phys. Rev. A 79, 062303 (2009). [4] A. Zavatta, V. parigi, M. S. Kim and M. Bellini, New J. Phys. 10, 123006 (2008).

New ideas on quantum process tomography Juan Pablo Paz

Department of Physics, FCEyN, University of Buenos Aires,

Argentina email: paz@df.uba.ar

Quantum process tomography (QPT) is an esential task to achieve quantum information processing. In fact, the design of good quantum error correction strategies to achieve the desired degree of quantum control requires the appropiate characterization of quantum errors. QPT is a hard task since it requires, in its full form, resources scaling exponentially with the number of qubits in the system. In this talk I will review the standard methods for quantum process tomography and describe recent progress in this field presenting algorithms that achieve partial characterization of quantum processes using resources that scale polynomically with the number of qubits. I will discuss some experimental implementations of such methods with single photons.

A macroscopic singlet Bell state of light Gerd Leuchs1,3, Timur Sh. Iskhakov1,3, and Maria V. Chekhova1,2 1Max Planck Institute for the Science of Light, Günther-Scharowsky-Strasse 1/Bau 24, 91058 Erlangen, Germany 2Department of Physics, M.V.Lomonosov Moscow State University, Leninskie Gory, 119991 Moscow, Russia 3Institute of Optics, Information and Photonics, University Erlangen-Nuremberg, Staudtstrasse 7/B2, 91058 Erlangen, Germany Two-photon Bell states are among the basic tools of quantum optics and quantum information. Currently, there is a growing interest in their macroscopic analogues in connection with macroscopic entanglement. Among the macroscopic Bell states, the singlet state is especially interesting as it possesses two remarkable properties. First, being pure, it is fully non polarized, i.e., invariant to all polarization transformations. Second, it has no polarization noise, i.e. for this particular state the variances of all Stokes observables are equal to zero. Although predicted long ago [1], the macroscopic singlet Bell state has not been observed before. Here we report on its production in a set-up resembling the one for two-photon Bell state generation but with stronger pumping, providing macroscopic photon numbers and hence allowing for efficient direct detection. Simultaneous suppression of fluctuations in three Stokes observables below the shot-noise limit is demonstrated, opening perspectives for noiseless polarization measurements [2]. The macroscopic singlet Bell state is also shown to be invariant to polarization transformations, unlike the other macroscopic Bell states, which manifest hidden polarization [3-5], i.e., are only polarized in the second and higher orders in the intensity but not in the first order [6]. [1] V. P. Karassiov, J. Phys. A 26, 4345 (1993). [2] M. Koschorreck et al., Phys. Rev. Lett. 104, 093602 (2010). [3] D. N. Klyshko, JETP 84, 1065 (1997). [4] P. Usachev et al., Opt. Commun. 193, 161 (2001). [5] A. Sehat et al., Phys. Rev. A 71, 033818 (2005). [6] A. B. Klimov et al., Phys. Rev. Lett. in press 2010, arXiv:1004.3283 (2010).

Excitations and Characterization of an Atomic Superfluid: emergence of turbulence

and characterization

V.S. Bagnato

Instituo de Fisica de Sao Carlos – Univeristy of S. Paulo

São Carlos – SP - Brazil

(Work done in collaboration with the following students and PD: E. Henn, J. Seman, P. Castilho,

G. Roati, K. Magalhaes, R. Shiozaki, E. Ramos, M. Caracanhas, C. Castelo-Branco, P.Tavares , G.

Bagnato, F. Jackson, F. Poveda, G. Telles, and the participation of external collaborators: A.

Fetter, V. Yukalov , V.Romero-Rochin, M. Kobayashi, K. Kasamatsu and M. Tsubota)

In this presentation we review our technique to generate turbulence in a BEC, where a

perturbation in the trapping potential produces displacement, rotation and deformation of the atomic

cloud. The generation of quantized vortices is investigated as a function of the amplitude of

oscillation as well as time of excitation. The results allow the construction of a diagram for stable

structures justified based on numerical simulations using the Gross-Pitaevskii equation. The

necessity of having the presence of dissipation is obtained during the numerical simulation.

Hydrodynamic considerations allow us to understand the occurrence of an anomalous expansion

behavior for the cloud within the turbulent regime. Concepts of thermodynamic are applied to

understand the variation of pressure during the occurrence of turbulence in the condensate. The

existence of a critical number of vortices as a threshold for turbulence is also discussed. (

Experimental part with Financial fupport from FAPESP and CNPq – Brazilian agencies) .

Density distribution for a turbulent cloud

Mechanical properties of propagation invariant beams and their effect in cold atoms

Rocío Jáuregui

IF-UNAM

The generation of optical fields that maintain their transverse structure over long distances has increased the interest in their theoretical and experimental study. Explicit expressions are known for four symmetries: rectangular (plane waves), circular (Bessel waves), elliptic (Mathieu waves) and parabolic (Weber waves). It is well known that the mechanical variable directly associated to plane waves is the linear momentum. The photons associated to Bessel waves can carry a well defined orbital angular momentum. In this work, explicit expressions are given for the mechanical properties of Mathieu and Weber electromagnetic fields. The density of these mechanical variables are shown to be given by products of second order derivatives of the electric and magnetic fields of the wave and can be interpreted as densities of products of linear and angular momenta. The possibility that these mechanical properties can be transferred to cold atoms in optical lattices built from these structured beams is numerically explored. We concentrate on the quasi conservative red detuned far-off-resonance regime. We also show that the atoms dynamics in this structured lattices is non trivial. The system exhibits quasi periodic and chaotic behaviors which can be controlled by varying the intensity of the beams. The presence of Levy-like flights on the transverse plane of the lattice, as well as the spectral density of the trajectories are used as chaos signatures. Finally we propose a scheme to split a cloud of thermal atoms using a Weber beam.

Generation and characterization of photon pairs with optimized entanglement characteristics for quantum information processing

applications.

Alfred U'Ren.

ICN-UNAM

In this talk we describe recent work -- both theoretical and experimental -- aimed at the generation and characterization of photon pairs with optimized entanglement properties. Our work covers photon pair generation through spontaneous parametric downconversion in nonlinear crystals as well photon pair generation through spontaneous four wave mixing in optical fibers.

We are interested in the generation of two-photon states with spectral properties ranging from factorable to highly entangled, and from quasi-monochromatic to ultra-broadband. We also report the use of upconversion as a tool for the temporal characterization of entangled photon-pairs.

Entanglement entropy of symmetry adapted statesin the Dicke Model

O. Castanos, E. Nahmad-Achar, R. Lopez-Pena, J.G. Hirsch

We show that the Dicke Hamiltonian is invariant under the point groupC2 = {I, exp (iπΛ)} with Λ the excitation number operator, which counts thenumber of photons plus the number of excited atoms. This invariance, togethera variational procedure with trial states constituted by the tensorial product ofWeyl and SU(2) coherent states, allows us to get analytical expressions for theground and first excited states of the model. These analytical states are polyno-mial functions depending on the atomic frequency and the coupling strenght ofthe matter-field interaction, in units of the frequency of the one mode electro-magnetic field. Their corresponding fidelities with the states obtained from theexact diagonalization of the Hamiltonian matrix are very close to one, except inthe region of the parameter space close to the quantum phase transition of thenormal to super-radiant behavior of the atoms. We determine the statisticalproperties of matter and field observables by calculating their matrix elementswith respect to the mentioned states with an even or odd number of excitations.Finally, the entanglement entropy between the matter and field degrees of free-dom are evaluated as a function of the coupling parameter. All the observablestogether with the entanglement entropy exhibit a clear singular behavior acrossthe quantum phase transition.

Non-Markovian decoherence in donor-based charge quantum bits

F. Lastra, S. Reyes, S. Wallentowitz

Departamento de Física, Facultad de Física, Pontificia Universidad Católica

de Chile

A model for the dynamics of donor-based charge qubits with electron-phonon interaction is developed. The decoherence of the qubit is analytically obtained and shown to reveal non-Markovian features: The decoherence rate varies with time and attains negative values, generating a non-exponential decay of the electronic coherence and a later recoherence. The resulting coherence time is inversely proportional to the temperature, thus leading to low decoherence below a substrate dependent characteristic temperature.

Squeezed in n qubit system

A.B. Klimov, C. Muñoz

Departamento de Fisica, Universidad de Guadalajara, 44420 Guadalajara,

Jalisco, Mexico

We show that 2n "coherent" states of an n-qubit system, generated by application of the discrete displacement operator to a symmetric feducial state have isotrppic fluctuations in a specific "tangent" plane. This allows to use them as reference states to define discrete squeezing. States with reduced fluctuations can be obtained by using XOR operators to correlate qubits.

The quantum phase problem in relativistic theories

J. Sperling∗ and W. Vogel

Arbeitsgruppe Quantenoptik, Institut fur Physik,

Universitat Rostock, D-18051 Rostock, Germany

Abstract – In 1927 P. A. M. Dirac failed to provide a consistent quantum description

of the phase of a radiation field [1]. The Hermitian phase operator Φ is considered to

fulfill commutation relation [Φ, n] = −i, where n is the photon number operator. Only

one year after formulating the quantum phase problem, Dirac developed the theory of the

electron, which led to the anti-particle – the positron. Within this description particle and

anti-particle can be transformed into each other by changing the direction of time.

We study Dirac’s phase problem in the context of Lorenz invariant theories. The usual de-

scription of the phase operator does not include the time reversal transformation. Especially

the effect on the choice of an appropriate Hilbert space in connection to this transformation

will be considered. We will show that an additional degree of freedom occurs. Similarly to

the introduction of the anti-particle of the electron, we obtain a spinor representation with

components for both the photon and the corresponding anti-photon. This additional degree

of freedom can be used for a corrected quantum description of the phase of a radiation

field [2]. It also leads to new insight into the quantum measurement of time.

[1] P. A. M. Dirac, The Quantum Theory of the Emission and Absorption of Radiation. Proc. R.

Soc. Lond. A114, 243 (1927).

[2] J. Sperling and W. Vogel, Dirac’s Quantum Phase Problem, e-Print arXiv:0907.3349 [quant-ph].

∗Electronic address: jan.sperling2@uni-rostock.de

Single Molecule Magnets

Jorge A. Campos, Jorge G. Hirsch

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,

Apdo. Postal 70.543 México 04510 D.F. Single-molecule magnets (SMMs) are polynuclear metal complexes which exhibit superparamagnetic properties similar to nanoscale magnetic particles (nanomagnets). They have large spin in their ground state arising from antiferromagnetic interactions between the spin of the metalic ions. When a sample is exposed to a large external magnetic field at very low temperatures, the magnetization saturates. If the external field is turned off, a remanent magnetization is observed, which very slowly tends to the equilibrium value. For this reason nanomagnets are promising candidates for the construction of quantum computers. Electron paramagnetic resonance (EPR) studies provides extensive information about the energy spectra and the transition strengths between SMM quantum states with different alignments. A simple generalization of the Lipkin-Meshkov-Glick (LMG) Hamiltonian allows for the description of the SMM as microscopic giant rotors. In the case of 8Fe SMM a detailed comparison is presented of the observed absorption strengths and the theoretically predicted one, which have a remarkably good agreement. It opens the possibility to observe the quantum phase transitions predicted in the LMG model in the SMM.

Entanglement properties of an ultracold atom interacting with a quantum cavity electromagnetic field

Luis Octavio Castaños and Rocío Jáuregui

IF-UNAM

We study the temporal evolution of the properties of a two level atom coupled to a single-mode cavity-field without dissipation with its center of mass motion quantized in one dimension. It is shown that, starting with a separable state, genuine tripartite entangled states can be generated under resonance conditions of the light frequency and atom transition frequency in the cold regime. The onset of Rabi oscillations is analyzed and explicit predictions for properties like emission probability and dispersions for the center of mass position and momenta are given for resonance and detuned conditions. Transmission-resonance effects on entanglement and other properties are also analyzed. Comparisons with the semi-classical adiabatic approximation predictions are also made.

Studiyng The dynamics of entanglement in qubit systems

Osvaldo Jimenez Farias (Instituto de Ciencias Nucleares, UNAM) Laboratorio de optica Quantica IF- UFRJ Rio de Janeiro, Brasil. Tel

(55)(21)25627466.

ofarias@nucleares.unam.mx, ofarias@if.ufrj.br

G. Aguilar, C. Lombard, S.P. Walborn, P.H. Souto Ribeiro,

Luiz Davidovich.

The estimation of the entanglement of multipartite systems undergoing decoherence is important for assessing the robustness of quantum information processes. It usually requires access to the final state and its full reconstruction through quantum tomography. General dynamical laws may simplify this task. We found that when one of the parties of an initially entangled two-qubit system is subject to a noisy channel, a single universal curve describes the dynamics of entanglement for both pure and mixed states, including those for which entanglement suddenly disappears. Our result, which is experimentally demonstrated using a linear optics setup, leads to a direct and efficient determination of entanglement through the knowledge of the initial state and single-party process tomography alone, foregoing the need to reconstruct the final state.

In addition we present recent results concerning the existence of invariant quantities under the interaction of a qubit with its enviroment. Such quantities are usefull in deriving equations which seems to impliy the existence of invariance of bipartite entanglement in multiquibit systems.

Ion-laser interaction in all regimes

A. Zúñiga-Segundo1 and H. Moya-Cessa2

1IPN, Mexico 2INAOE, Mexico

We show that in the trapped ion-laser interaction all the regimes may be considered analytically. We may solve not only for different laser intensities, but also away from resonance and from the Lamb-Dicke regime. It is found a dispersive Hamiltonian for the high intensity regime, that, being diagonal, its evolution operator may be easily calculated.

NUMERICAL SOLUTIONS TO THE DICKE HAMILTONIAN Miguel Angel Bastarrachea, Jorge G. Hirsch

Instituto de Ciencias Nucleares, UNAM.

We study the exact numerical solutions of the Dicke Hamiltonian, which describes a system of many two level atoms interacting with a monochromatic radiation field into a cavity. The Dicke model is an example of a quantum collective behavior which shows “superradiant” quantum phase transitions in the thermodynamic limit. Results obtained employing two different bases are compared. Both of them use the “pseudospin” base to describe the atomic states. For the photon states we use in one case Fock states, while in the other case we use annihilation operators shifted by a factor proportional to Jz, which have coherent states as their vacua, and powers of the shifted creation creation operator acting over the coherent state. It is shown that, when the number of atoms increases the description of ground state of the system in the superradiant phase requires an exponentially growing number of photons to be included. This imposes a strong limit to the states that can be solved exactly. In the coherent state bases the number of excitations coupled with the atoms decrease when the atomic number increases, allowing calculations that are very difficult in the other base. We show results for observables of the system like the energy, the photon number and the number of atoms in the upper state in each base. These quantities are studied using the base state and the first excited state.

Calibration of a High Detection Efficiency Transition Edge Sensor Photon-

Number-Resolving Detector for Quantum Information Applications

F. E. Becerra1,2

, M. Nadeau2,3

, J. Fan1,2

, S. Polyakov1,2

, and A. Migdall1,2

1 Optical Technology Division, National Institute of Standards and Technology

100 Bureau Drive, Gaithersburg, MD 20899-8441, USA 2 Joint Quantum Institute, University of Maryland, College Park, MD 20742, USA

3 American University, 4400 Massachusetts Avenue, NW, Washington, DC 20016, USA

Transition Edge Sensors (TESs) are single-photon detectors with advantages over conventional

Avalanche Photo Diodes. Low noise, photon-number-resolving capabilities, and high detection

efficiency are characteristics that make them very attractive for quantum information and

quantum communication applications, as well as for fundamental tests of nature. Because of their

wide-band detection ability, from 350 nm to 2 μm, and high detection efficiency at

telecommunication wavelengths* TESs can be used for long distance quantum communications

and secure quantum key distribution. Their near-unity detection efficiency and photon-number

resolution makes them an excellent tool for testing and characterizing single-photon sources and

for multi-photon non-classical state preparation. However, any inefficiency of the detector or

erroneous estimation of its detection efficiency will affect the characterization of a source.

The measurement of the detection efficiency of TESs requires low repetition rates, ≈ 50 kHz, due

to the slow recovery time (≈ 2 s) of the detector. This forces the light source used for the

calibration to have an average intensity in the femtowatt range, making it very challenging to

calibrate the source for this measurement. We describe our efforts to determine the detection

efficiency of a near-unity efficiency device. This work involves comparison to calibrated transfer

standard detectors in both free-space and fiber-coupled formats.

*Adriana E. Lita et al., Optics Express, Vol. 16, Issue 5, pp. 3032-3040 (2008).

Quantum walk in an optical feedback loop with reflections

Aurel Gabris, A. Schreiber, K.N. Cassemiro, V. Potocek, I. Jex, Ch. Silberhorn

Department of Physics, FNSPE, Czech Technical University in Prague, Brehova 7, 115 19 Praha, Czech Republic

gabris.aurel@fjfi.cvut.cz

We present a detailed analysis of a robust implementation of a coined quantum walk along a line using only passive optical elements. At the core of our realization is a polarization dependent fiber optical delay line embedded in a loop network which allows to keep the amount of required resources constant as the walker’s position Hilbert space is increased. Thus the polarization of the photon plays the role of a two dimensional coin, and the walker position corresponds to time-bin photons. Our analysis of the experimental signal shows negligible level of decoherence, but a significant contribution of coherent errors in form of reflections occurring inside the feedback loop. The impact of these reflections are two fold: firstly they introduce an increased loss rate per round trip thus limiting visibility for more than 5 iterations, secondly, they produce additional peaks in the output signal some partially overlapping with the expected peaks. For the analysis we employ a model based on the idea that a one dimensional quantum walk with a four dimensional coin is realized, provided the reflections occur at appropriate locations. The existence of a higher dimensional coin operator raises interesting questions such as localisation and recurrence behaviour. The comparison with the experimental signal requires a careful treatment, since the setup allows the direct measurement only one of the two dimensional subspaces of the coin operator, and for the other coin states only indirect data is available.

Controlled dynamical generation of arbitrary two-qubit state

Malena Hor-Meyll, Adriana Auyuanet and Fernando de Melo

Laboratory of Quantum Optics and Quantum Information Fluminense Federal University

Av. Gal. Milton Tavares de Souza S/N 24210-346 - Niteroi - RJ - BRAZIL

malena@if.uff.br We present a scheme for generating arbitrary two-qubit mixed states using an all-optical setup. The strategy to obtain a target mixed state is to force one of the qubits to interact with a specific environment. The flexibility of our experimental arrangement allows for the study of the dynamics of quantum states under generic decoherence processes. Taking into account the difficulty of preserving genuine maximally entangled pure states during system evolution, this source of mixed states can be a useful tool to test real quantum computation and quantum information protocols.

Death and revival of an electromagnetically induced transparency in hot alkali gases

O.S. Mishina, M. Scherman, P.Lombardi, J. Orrtalo, J. Laurat, E. Giacobino

Laboratoire Kastler Brossel, Université Pierre et Marie Curie, Ecole Normale Supérieure,

CNRS, Case 74, 4 place Jussieu, 75252 Paris Cedex 05, France

D.V. Kupriyanov

Department of Theoretical Physics, State Polytechnic University, 29 Politekhnicheskaya St., 195251, St.-Petersburg, Russia

Electromagnetically induced transparency (EIT) provides a tool to control the transfer of quantum states between light and matter. In the general picture, EIT involves two different light fields, a signal and a control, and a three-level atomic system. Such a model is widely studied theoretically and applied for the explanations of most of experimental results. However, in many materials (like atomic gases, rare-earth doped crystals, NV-centers in diamonds and quantum dots) the level structure is more complicated. Instead of one excited state as in the standard three-level lambda configuration, additional excited states play an important role in the Raman process. This leads to significant modifications in the light-atom interaction. Such effects are the topic of the work presented here, both from a theoretical and an experimental point of view. First, we theoretically found that the hyperfine splitting can cause detrimental reduction of the EIT in the alkali-metal vapour due to constructive or destructive interferences of several $\Lambda$-transitions. Our model is in very good agreement with experiments performed in our group with vapors of Cs atoms. We then propose and implement a method to enhance the transparency in this system via effective cooling by optical pumping. An enhancement of the EIT contrast by a factor of $4.3$ has been experimentally observed.

Experimental Observation of Genuine Non-Gaussian Entanglement

Fabricio Toscano, R. M. Gomes, A. Salles, P. H. Souto Ribeiro and S. P. Walborn

Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ, 21941-972, Brazil.

toscano@if.ufrj.br

Most of the attention given to continuous variable (CV) systems for quantum information processing has traditionally been focused on Gaussian states. Gaussian entanglement is readily produced in the laboratory, and has been used to teleport quantum states between two parties. However, non-Gaussianity is an essential requirement for universal quantum computation and entanglement distillation and can improve the realization of quantum teleportation and quantum cloning. These advantages have led to the consideration of non-Gaussianity as a resource in its own right. We report the experimental observation of genuine non-Gaussian entanglement using spatially entangled photon pairs produced by the spontaneous parametric down-conversion (SPDC). We show that the quantum correlations are invisible to all tests which identify Gaussian entanglement, and are revealed only under application of a higher-order entanglement criterion (i.e. the Shchukin-Vogel inseparability criteria for bipartite CV entanglement). Thus, the photons exhibit a varitey of entanglement which cannot be reproduced bygaussian states.

Creation of Entanglement of two Atoms Coupledto two Distant Cavities with Losses

Victor Montenegro and Miguel OrszagFacultad de Fısica, Pontificia Universidad Catolica de Chile, Casilla 306, Santiago, Chile

AbstractThe present model describes the evolution of two circular Rydberg

atoms [1] in two distant cavities connected by an optical fiber. Toinclude losses both in the cavities and fiber, we use the MicroscopicMaster Equation [2–4], where Jumps Operators are transitions betweenthe six eigenstates of the full Hamiltonian.If we chose equal coupling constants, the peaks of C(t) versus t arenarrow. In order to improve the time-plateau, we choose different cou-pling constants [5]. However, an impressive improvement is obtained,for circular Rydberg atoms with atomic frequencies of 51 GHz (Bruneet al.) when the field is detuned by the order of 1MHz - 100MHz, infact we show that in presence of dissipation the time-plateau increaseswith increasing detuning.We investigate the time it takes to generate the first plateau versus theatom-cavity detuning, we noticed that as the detuning increases theplateau takes longer to generate.We show that the concurrence of the first time-plateau decreases sloweras we increase the detuning, this relation of inverse proportionality ap-pears for certain dissipation [6], we choose τcav = 125ms, τfib = 10ms.In consequence, if we want a wide plateau, we must pay the cost ofwhich will be generated with a slower and less concurrence. Finally,we show that the scheme is robust against the mixed states.

References

[1] Z.-R. Zhong, Opt. Commun. (2010), doi:10.1016/j.optcom.2009.12.052

[2] M.-Wilczewski and M.-Czachor, Phys. Rev. A 79, 033836 (2009)

[3] M.-Scala, B.-Militello, A.-Messina, J.-Piilo and S.-Maniscalco, Phys. Rev. A 75,013811 (2007)

[4] H.-P. Breuer and F. Petruccione, The Theory of Open Systems (Clarendon, Oxford,2006)

[5] S.-Natali and Z.-Ficek, Phys. Rev. A 75, 042307 (2007)

[6] S.-Kuhr, S.-Gleyzes, C.-Guerlin, J.-Bernu, U.-B.-Hoff, S.-Deleglise, S.-Osnaghi, M.-

Brune and J.- Raimond, S.- Haroche, E.-Jacques, P.-Bosland and B.-Visentin, App.

Phys. Lett. 90, 164101 (2007)

Phase locked lasers for EIT José Juan Ortega Sigala, Eduardo Gómez García

Instituto de Física, Universidad Autónoma de San Luis Potosí

We are interested in studying the photon correlations produced in Electromagnetic Induced Transparency (EIT). The correlations can be used to distinguish EIT from the Autler-Townes splitting which is an incoherent process that under some conditions produces a signal similar to EIT. The observation of Electromagnetically Induced Transparency requires two phase locked laser beams at specific frequencies. The two laser beams are typically generated from independent sources that are electronically locked using an optical phase locked loop (OPLL). We demonstrate the generation of phase locked beams generated by amplitude modulation of a single beam. We send the laser through a fiber amplitude modulator to create sidebands. We measure the phase stability of the sidebands with respect to the carrier, and we find that it is limited by the stability of the source producing the modulation. The optical generation of phase locked beams removes the large bandwidth requirement of traditional locking systems. In addition it opens the possibility of changing the relative phase of the two beams in a very short time to move away from the steady state and study the dynamics back to the dark state. We obtain sideband powers larger than 30% (10%) for modulation frequencies lower (higher) than 1GHz. The power of the beam is boosted by a tapered amplifier constructed in our laboratory. We analyze the case of modulation of the laser beam by directly modulating the current feeding the amplifier. The phase locked beams will be further used in our laboratory to induce Raman transitions between hyperfine states in a rubidium magneto-optical trap.

Poster presentation

José Juan Ortega Sigala

Address: Av. Manuel Nava 6 Zona Universitaria 78290, San Luis Potosí SLP, México

Email: jjosila@hotmail.com

Eduardo Gómez García

Address: Av. Manuel Nava 6 Zona Universitaria 78290, San Luis Potosí SLP, México

Email: egomez@ifisica.uaslp.mx

PHOTON PAIR SOURCES BASED ON OPTICAL FIBERS

Karina Garay-Palmett1, Alfred B. U’Ren1 and Raúl Rangel-Rojo2

1Instituto de Ciencias Nucleares. Universidad Nacional Autónoma de México, UNAM (México) 2Departamento de Óptica. Centro de Investigación Científica y de Educación Superior de

Ensenada, CICESE (México) karina.garay@nucleares.unam.mx, alfred.uren@nucleares.unam.mx

The fast growing field of photonic quantum technology promises drastic enhancements in

performance with respect to classical alternatives. However, in order to realize this potential we must first develop non-classical light sources with specific properties and which are compatible with existing optical fiber networks. In optical fibers, parametric processes arising from the third-order electrical susceptibility offer promising alternatives for this aim. Specifically, in recent years there has been a growing interest in developing photon-pair sources based on optical fiber, in which the generation mechanism is the process of spontaneous four-wave mixing (SFWM). These sources can be remarkably bright because of the long interaction lengths possible in fibers and because the emitted flux scales as the square of the incident pump power. On the other hand, fiber dispersion properties may be readily engineered resulting in tailored photon-pair entanglement properties as we demonstrated in Ref. [1]. Actually, photonic crystal fibers (PCF) constitute a flexible system that can generate two-photon states with different degrees of spectral correlation, particularly factorable states and highly correlated states, as it is shown in figure 1.

Figure 1. a) Phase-matching orientation angle, which determines the spectral correlation degree of the two-photon states. b) Joint spectral intensity of a factorable state. c) Joint spectral intensity of a highly entangled two-photon state.

We have developed a exhaustive theoretical study of the SFWM, restricting it to

configurations in which the four interacting fields have the same polarization and propagate in the same direction along the optical fiber. The study includes the photon-pair generation process with monochromatic and pulsed pumps. Our results have contributed significantly to the experimental implementation of two-photon sources with tailored spectral properties [2]. More recently, we have been interested in extending our theory to different SFWM configurations and likewise determine conditions that lead to the simultaneous emission of multiple photons in optical fibers.

References [1] K. Garay-Palmett, et al., Opt. Express 15, 14870-14886 (2007). [2] C. Söller, et al., Phys. Rev. A 81, 031801 (2010).

Quantum state reconstruction of a squeezed laser field by unbalanced homodyning

Birger Seifert and Sascha Wallentowitz

Contact address: Facultad de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile

bseifert@fis.puc.cl

Balanced homodyning is the standard technique for the reconstruction of thequantum state of a radiation mode [1]. Unfortunately, the mathematical procedure for the reconstruction is based on the inverse Radon transform. This transform requires considerable processing performance and is not robust against noisy data. Unbalanced homodyning combined with phase-randomized balanced homodyning (cascaded homodyning) is a suitable approach to overcome the shortcomings of balanced homodyning [2]. An experiment with quadrature-squeezed light emitted by a semiconductor laser is discussed. The density-matrix reconstruction via cascaded homodyning requires a phase-randomized local oscillator. The phase difference of succeeding laser pulses has been used, which is based on spontaneous emission [3]. This approach requires coherent laser pulses, which is a serious drawback. Therefore, the control of the local oscillator phase and phase randomization in general is the main topic of discussion. [1] D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, "Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum", Phys. Rev. Lett. 70, 1244 (1993) [2] Z. Kis, T. Kiss, J. Janszky, P. Adam, S. Wallentowitz, W. Vogel, "Local sampling of phase-space distributions by cascaded optical homodyning", Phys. Rev. A 59, R39R42 (1999) [3] M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, "Photon-number statistics from the phase-averaged quadrature-field distribution: Theory and ultrafast measurement", Phys. Rev. A 52, R924R927 (1995).

Quantum Degrees of Polarization and Unpolarized States

Jonas Soderholm,1, ∗ Gunnar Bjork,2 Luis L. Sanchez-Soto,3 and Andrei B. Klimov4

1Max Planck Institute for the Science of Light, Gunther-Scharowsky-Str. 1, 91058 Erlangen, Germany2School of Communication and Information Technology, Royal Institute of Technology (KTH),

Electrum 229, SE-164 40 Kista, Sweden3Departamento de Optica, Facultad de Fısica, Universidad Complutense, 28040 Madrid, Spain

4Departamento de Fısica, Universidad de Guadalajara, 44420 Guadalajara, Jalisco, Mexico

Despite that the operators corresponding to the Stokes parameters were identified long ago, it is still not clear howto quantify polarization in quantum optics. Denoting the annihilation operators of the modes with horizontal andvertical polarization as a and b, respectively, the Stokes operators can be expressed as

S0 = a†a + b†b , Sx = ab† + a†b , Sy = i(ab† − a†b) , Sz = a†a− b†b , (1)

Since the Stokes parameters are given by the average values of these operators, the classical degree of polarizationbecomes

PS =

√〈Sx〉2 + 〈Sy〉2 + 〈Sz〉2

〈S0〉. (2)

However, there exist quantum states that obviously carry some information about polarization, but have a vanishingdegree of polarization according to this definition [1]. Many quantum degrees of polarization have therefore beenproposed. However, they are all known to suffer from different drawbacks. In order to satisfactory quantify polarizationin quantum optics, we believe that it is necessary to introduce a hierarchy of polarization degrees [2]. Such a hierarchyhas been suggested by Klyshko [3], but those degrees do not have the desirable property of SU(2) invariance.

Here, we take a SU(2)-invariant approach to the problem by introducing a hierarchy of unpolarized states, in away similar to that of Zimba [4]. The corresponding classes of unpolarized states represent a connection between thestates that are unpolarized according to Eq. (2), and the SU(2)-invariant states [5, 6], which are considered to beunpolarized in quantum optics. However, all our classes differ from these sets of classically and quantum mechanicallyunpolarized states. The introduced states imply nice symmetry properties of the generalized coherence matrix [3]of corresponding order. We also discuss how this approach could be generalized to obtain a hierarchy of degrees ofpolarization.

∗ Electronic address: jonas.soederholm@mpl.mpg.de[1] D. N. Klyshko, Phys. Lett. A 163, 349 (1992).[2] A. B. Klimov et al., arXiv:1004.3283.[3] D. N. Klyshko, Sov. Phys. JETP 84, 1065 (1997).[4] J. Zimba, Elect. J. Theor. Phys. 3(10), 143 (2006).[5] H. Prakash and N. Chandra, Phys. Rev. A 4, 796 (1971).[6] G. S. Agarwal, Lett. Nuovo Cimento 1, 53 (1971).

Selective and Efficient Quantum Process Tomography with Single Photons.

Christian Schmiegelow, Ariel Benderski, Miguel Larotonda, Juan Pablo

Paz

Instituto de Física de Buenos Aires; Departamento de Física, FCEyN, UBA. schmiegelow@df.uba.ar

We present experimental results demonstrating a photonic implementation of an efficient quantum algorithm that estimates any parameter characterizing an arbitrary quantum process. The algorithm, introduced first in [PRL100,190403(2008)] not only enables estimation of selected parameters using polynomial resources but also can be used to efficiently determine all the elements of the $\chi$--matrix that are larger than a fixed value. In our laboratory we performed full and partial quantum process tomography on a channel affecting the qubit encoded in the polarization of single photons [PRL104,123601(2010)]. Here, we report new results for the quantum process tomography on a channel affecting two qubits, encoded in the polarization and the path degrees of freedom of single photons generated by parametric down conversion. We compare our results with the ones obtained using standard quantum process tomography showing that for the two--qubit channel the new selective method is already more efficient than the standard one.

The Relative Phase Gate

L. M. Arévalo Aguilar

In this work we define the relative phase gate, which is a two qubit gate. We show the kind of entangled stated that this phase gate produces and study its characteristics by comparison with others entangled states. Finally, we show that the definition of the relative phase gate can be expanded to three qubits.

Rate analysis for a hybrid quantum repeater

Nadja K. Bernardes1, Ludmila Praxmeyer2, and Peter van Loock11Optical Quantum Information Theory Group, Max Planck Institute for the Science of Light,

Gunther-Scharowsky-Str. 1/Bau 24, 91058 Erlangen, GermanyInstitute of Theoretical Physics I, Universitat Erlangen-Nurnberg, Staudttr. 7/B2, 91058 Erlangen, Germany and

2Institute of Physics, Nicolaus Copernicus University, ul. Grudziadzka 5, 87-100 Torun, Poland

We present a detailed rate analysis for a hybrid quantum repeater assuming perfect memories and the existenceof optimal entanglement generation probabilities and deterministic swapping routines. The quantum repeaterprotocol is based on atomic qubit-entanglement distribution through optical coherent-state communication. Anexact formula for the rate of entanglement generation in quantum repeaters is provided as well as a study aboutthe impacts of entanglement purification and multiplexing strategies. In a feasible experimental scenario, oursystem can achieve rates of 100 pairs per second for a total distance of 1280 km.

We analysed the rates to distribute an entangled state for aquantum repeater [1, 2] based on atomic qubit-entanglementdistribution through optical coherent-state communication(hybrid quantum repeater [3]). In particular we considerednonlocal distribution of two-qubit entangled memory pairsbased on unambiguous state discrimination (USD) measure-ments of coherent states [4]. This scheme provides a clearrelation between the probability of success P0 of generationand the fidelity F of the entangled state:

P0 = 1− (2F−1)η/(1−η). (1)

Photon losses are considered to be the main source of errorand they will be described as a beam splitter with transmissiv-ity η. Entanglement purification and swapping, the two essen-tial tools for the quantum repeater, can be performed using thesame interaction described above [5]. Another important toolin the architecture of the QR is memory and it will be consid-ered in this analysis as perfect (infinite decoherence time).

Let us first consider a general quantum repeater. A total dis-tance L is divided in 2n segments, each of length L0 = L/2n.First entanglement is generated between the adjacent nodes,which is accomplished with probability P0. Then these seg-ments are connected, extending the entanglement from L0 to2L0. This is performed many times, until the terminal nodes,separated by L = 2nL0, are entangled. The rate to successfullygenerate entanglement in all of 2n pairs over L will be givenby

Rn =1

T0Zn(P0), (2)

where

Zn(P) =2n

∑j=1

(2n

j

)(−1) j+1

1− (1−P) j (3)

and T0 = 2L0/c is the minimum time to successfully generateentanglement over L0, considering that this is the time spenton classical communication to verify the success of the entan-glement generation over L0 and c is the speed of light. Com-monly in the literature [6], for small P0, these rates are approx-imated by P0

T0

( 23

)n. However, for a total distance of L = 1280

km and L0 = 20 km, we verified that the approximate formulais underestimating the rates by more than 50%.

We also analysed the effect of purification in the rates. Weobserved that the increase of rounds of purification will notalways be associated with an increase in the rates. Anotherapproach that improves the rates is multiplexing the quantumnodes. In the parallel repeater, the ith memory element pairin one node interacts only with the ith pair in other nodes,however, for the multiplexing scheme, resources can be dy-namically allocated. We showed that although multiplexingimproves our rates, compared to purification, this improve-ment is modest and multiplexing will not be considered in ouranalysis.

We showed that for the hybrid quantum repeater with USDmeasurements [4], for just 4 qubits per half node, two roundsof purification in the first nesting level, L = 1280 km andL0 = 20 km, a rate of circa 119 pairs per second with F = 0.98can be achieved, an improvement of one order of magnitudecompared to the homodyne measurement scheme [3], where arate of 15 pairs per second with F = 0.98 was achieved. Notethat in our work, rates were obtained analytically, in contrastto the numerical simulation used in [3]. Moreover, multiplex-ing was omitted and only a minimal purification scheme al-lowed, which means we achieve our rates for a scenario whichis much closer to a practical implementation.

[1] H.-J. Briegel and et al., Phys. Rev. Lett. 81, 5932 (1998).[2] W. Dur and et al., Phys. Rev. A 59, 169 (1999).[3] P. van Loock and et al., Phys. Rev. Lett. 96, 240501 (2006).[4] P. van Loock and et al., Phys. Rev. A. 78, 062319 (2008).

[5] P. van Loock and et al., Phys. Rev. A. 78, 022303 (2008).[6] N. Sangouard and et al. (2009), arXiv:0906.2699v2.

Spatial correlations in quantum walks with two particles

M. Stefanak,1 S. M. Barnett,2 B. Kollar,3 T. Kiss,3 and I. Jex1

1Department of Physics, Faculty of Nuclear Sciences and Physical Engineering,Czech Technical University in Prague, Brehova 7, 115 19 Praha 1 - Stare Mesto, Czech Republic

2Department of Physics, University of Strathclyde,107 Rottenrow, Glasgow, G4 0NG, Scotland, U.K.

3Department of Quantum Optics and Quantum Information,Research Institute for Solid State Physics and Optics,

Hungarian Academy of Sciences, Konkoly-Thege u.29-33, H-1121 Budapest, Hungary

Over the years random walks proved to be a useful tool in many areas in physics as well as in other branches ofscience [1]. Quantum analogues of random walks have been proposed by Aharonov, Davidovich and Zagury [2]. Thequantum walks found a promising application in quantum information for the construction of fast search algorithms[3], which initiated considerable effort to understand all aspects of quantum walks [4]. Recently, a quantum walk ona line has been realized in various experimental settings, involving neutral atoms [5], ions [6] and photons [7].

Most of the studies to date considered quantum walks with a single particle. A natural extension of the field ofquantum walks is to involve more particles. This unlocks the additional features offered by quantum mechanics suchas entanglement and indistinguishability which are not available in classical random walks.

In the present contribution we consider the motion of two non-interacting particles performing a quantum walk ona line or a plane. We focus on the spatial correlations between the particles and the meeting problem [8]. Influence ofentanglement and indistinguishability on the motion of the particles are analyzed. Finally, we discuss the applicationof quantum walks involving more particles to experimental realizations of higher-dimensional quantum walks.

[1] N. Guillotin-Plantard, R. Schott, Dynamic Random Walks: Theory and Application, Elsevier, Amsterdam (2006)[2] Y. Aharonov, L. Davidovich, N. Zagury, ”Quantum random walks”, Phys. Rev. A 48, 1687 (1993)[3] N. Shenvi, J. Kempe, K. B. Whaley, ”Quantum random-walk search algorithm”, Phys. Rev. A 67, 052307 (2003)[4] G. Grimmett, S. Janson, P. F. Scudo,”Weak limits for quantum random walks”, Phys. Rev. E 69, 026119 (2004)[5] M. Karski, L. Frster, J. Choi, A. Steffen, W. Alt, D. Meschede and A. Widera, ”Quantum Walk in Position Space with

Single Optically Trapped Atoms”, Science 325, 174 (2009)[6] H. Schmitz, R. Matjeschk, Ch. Schneider, J. Glueckert, M. Enderlein, T. Huber and T. Schaetz, ”Quantum Walk of a

Trapped Ion in Phase Space”, Phys. Rev. Lett. 103, 090504 (2009)[7] A. Schreiber, K. N. Cassemiro, V. Potocek, A. Gabris, P. Mosley, E. Andersson, I. Jex and Ch. Silberhorn, ”Photons

Walking the Line: A Quantum Walk with Adjustable Coin Operations”, Phys. Rev. Lett. 104, 050502 (2010)[8] M. Stefanak, T. Kiss, I. Jex and B. Mohring, ”The meeting problem in the quantum walk” J. Phys. A 39, 14965 (2006)

Geometric phase with nonunitary evolution in presence of a quantum critical environment

F. Lombardo, F. Cucchietti, J-F. Zhang, P.I. Villar, and R. Laflamme

Departamento de Fisica, FCEyN - Universidad de Buenos Aires, Argentina

Geometric phases, arising from cyclic evolutions in a curved parameter space, appear in a wealth of physical settings. Recently, and largely motivated by the need of an experimentally realistic definition for quantum computing applications, the quantum geometric phase was generalized to open systems. The definition takes a kinematical approach, with an initial state that is evolved cyclically but coupled to an environment — leading to a correction of the geometric phase with respect to the uncoupled case. We obtain this correction by measuring the nonunitary evolution of the reduced density matrix of a spin one-half coupled to an environment. In particular, we consider a bath that can be tuned near a quantum phase transition, and demonstrate how the criticality information imprinted in the decoherence factor translates into the geometric phase. The experiments are done with a NMR quantum simulator, in which the critical environment is modeled using a one-qubit system.

CNOT on Polarization States of Coherent Light

Goce Chadzitaskos and Jiri TolarDepartment of Physics, FNSPE, Czech Technical University in Prague,

Brehova 7, 115 19 Praha 1, Czech Republic.

October 31, 2010

Abstract

We propose a CNOT gate for quantum computation. The CNOTis based on existence of triactive molecules, where in one directionit has dipole moment and cause rotation of the polarization plane oflinearly polarized light and in perpendicular direction it has a magneticmoment. The linearly polarized laser beam is divided into two beamsby beam splitter. In one beam is prepared a control state and the otherbeam is a target. The interaction of polarized states of both beamsin solution with triactive molecules can be described as interaction oftwo qubits in CNOT.

1

Entanglement witnesses for bipartite qutrit states

Alejandra Judith Gutiérrez Esparza

José Luis Lucio Martínez

División de Ciencias e Ingenierías Universidad de Guanajuato Loma del Bosque 103 Lomas del Campestre. C.P. 37150 León, Guanajuato. México

This project is focused on the construction, decomposition and a possible implementation of an entanglement witness (EW) for a two-qutrit state, a bipartite quantum state with a composite Hilbert space of 3x3. First, we describe three families of states and discuss a general scheme for the construction and decomposition of EW into locally measurable observables. Furthermore we use the SU(3) algebra to decompose the EW in proyectors which can be implemented experimentally in a straightforward way by using local projective measurement.

Optimal Teleportation Scheme for Noise Input States

Bruno G. Taketani, Ruynet Lima de Matos Filho, Fernando de Melo

Departamento de Fisica Matematica - Instituto de Fisica

Universidade Federal do Rio de Janeiro Caixa Postal 68528

21945-970 Rio de Janeiro - R.J. - Brazil

taketani@if.ufrj.br

Several studies have tackled the problem of teleportation when Alice and Bob share a non-maximally entangled state. Be that a pure [1] or mixed [2,3] state, protocols that aim to maximize the input/output fidelity have been suggested. Realistic experimental situations will nonetheless present decoherence not only in the quantum channel but also in the state to be teleported. We consider the problem of realistic teleportation of $d$-dimensional quantum states where neither the bipartite quantum channel nor the unknown input state are in a pure state. In the case of maximally entangled bipartite quantum channel a protocol that gives unit fidelity for pure and mixed input states can be easily established, but when the bipartite state undergoes a decoherence process knowledge of the space of states to be teleported is crucial to determine the optimal protocol. We study the case where this space of states is generated by a decoherence map applied to the space of pure states and we aim to maximize the fidelity between the teleportation output state and the original pure state. We present the optimal $d$-dimensional teleportation protocol when Alice is constrained to Bell-like projective measurements and no filtering operations are applied. Our protocol only requires knowledge of the bipartite state and the decoherence channel that acts on the input states. By calculating the optimal fidelity we arrive at a clear interpretation of the physically relevant condition that the optimal protocol must satisfy. Numerical results show that by taking into account the mixedness of the input state, our protocol outperforms other protocols [2] and the increase in fidelity can reach 10-20% in many cases.

[1] K. Banaszek, Phys. Rev. A 62, 024301 (2000). [2] S. Albeverio, S.-M. Fei and W.-L. Yang, Phys. Rev. A 66, 012301 (2002). [3] M. Horodecki, P. Horodecki and R. Horodecki, Phys. Rev. A 60, 1888 (1999).

The atom-field-mirror interaction

O. Aguilar Loreto1, D. Rodríguez-Méndez2 and H. Moya-Cessa2

1 U. de Guadalajara

2INAOE

We show how the interaction between a moving mirror interacting with a field that interacts with an atom can be simplified. We introduce a transformation that, with no approximation, produces a 2-system Hamiltonian that may be written, via small rotations, as an effective solvable one.

Complementarity of one- and two-photon interference for hybrid entangled states

W. A. T. Nogueira,1, 2, ∗ M. Santibanez,1, 2 S. Padua,3 A. Delgado,1, 2 C. Saavedra,1, 2 L. Neves,1, 2 and G. Lima1, 2

1Center for Optics and Photonics, Universidad de Concepcion, Casilla 4016, Concepcion, Chile.2Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion, Chile.

3Departamento de Fısica, Universidade Federal de Minas Gerais,Caixa Postal 702, Belo Horizonte, MG 30123-970, Brazil.

(Dated: July 15, 2010)

Recently, the experimental investigation of hybrid photonic entanglement (HPE), namely theentanglement between two different degrees of freedom of a photon pair, has been receiving a growingamount of attention [1–7]. In this work, we explore a source of HPE to study complementarityrelation for one- and two-photon visibilities, V 2

12 + V 21 ≤ 1 [8, 9], in such system. Here V1 represents

the one-photon visibility and V12 represents the two-photon visibility. This is an important issuesince there is an active interest in the understanding of complementarity [10] for multipartite andd-level states [11–16] from the experimental point of view.

Our HPE source is generated by exploring the polarization and spatial correlations of the photonpairs created in the process of parametric down-conversion along with the use of a single-photonbirefringent double slit and suitable spatial and polarization projections. Conditional and marginalprobabilities are calculated and they are used to obtain the corrected conditional probability, asintroduced in [8, 9]. This correction is necessary in order to interpret the values of two-photonvisibility as a scale, from 0, for a product state, until 1, for a maximum entangled state. Moreover,experimental results are showed for some produced hybrid entangled states, from which we extractedthe values of V1 and V12. It is important to note that it constitutes the first experimental observationof complementarity relation for the visibilities of one- and two-photon interference patterns for thiskind of state.

[1] M. Zukowsky, and A. Zeilinger, Phys. Lett. A 155, 69 (1991).[2] X.-s. Ma, A. Qarry, J. Kofler, T. Jennewein, and A. Zeilinger, Phys. Rev. A 79, 042101 (2009).[3] L. Neves, G. Lima, J. Aguirre, F. A. Torres-Ruiz, C. Saavedra, and A. Delgado, New J. Phys 11 073035 (2009).[4] L. Neves, G. Lima, A. Delgado, and C. Saavedra, Phys. Rev. A 80, 042322 (2009).[5] M. Fujiwara, M. Toyoshima, M. Sasaki, K. Yoshino, Y. Nambu, and A. Tomita, Appl. Phys. Lett. 95, 261103 (2009).[6] F. Bussieres, J. A. Slater, J. Jin, N. Godbout, and W. Tittel, Phys. Rev. A 81, 052106 (2010).[7] C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N.Y. Joly, P. Banzer, M. Fortsch, D. Elser, U. L. Andersen, Ch. Marquardt,

P. St.J. Russell, and G. Leuchs, arXiv:1007.1322v1 (2010).[8] G. Jaeger, M. A. Horne and A. Shimony, Phys. Rev. A 48, 1023 (1993).[9] G. Jaeger, A. Shimony and L. Vaidman, Phys. Rev. A 51, 54 (1995).

[10] N. Bohr, Nature (London) 121, 580 (1928).[11] M. Jakob and J. A. Bergou, Opt. Commun. 283, 827 (2010). arXiv: eprint quant-ph/0302075.[12] F. de Melo, S. P. Walborn, J. A. Bergou, and L. Davidovich, Phys. Rev. Lett. 98 250501 (2007).[13] X. Peng, X. Zhu, D. Suter, J. Du, M. Liu, and K. Gao, Phys. Rev. A 72, 052109 (2005)[14] M. Jakob and J. A. Bergou, Phys. Rev. A 76, 052107 (2007).[15] X. Peng, J. Zhang, J. Du, and D. Suter, Phys. Rev. A 77, 052107 (2008).[16] B. C. Hiesmayr and M. Huber, Phys. Rev. A 78, 012342 (2008).

∗Electronic address: wallon.nogueira@cefop.udec.cl

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Photonic qubit logic in multi-mode cavities

Mark S. Everitt and Barry M. Garraway We show that the interaction of multi-level atoms with multi-mode cavities can realise quantum gates when dual-rail photonic qubits are encoded on the cavity modes. The ancilla atoms transit the cavity. A universal set of gates is proposed, including the iSWAP operation.

Quantum limits for lossy optical interferometry

B. M. Escher, R. L. de Matos Filho, and L. DavidovichInstituto de Fısica, Universidade Federal do Rio de Janeiro, 21.942-972, Rio de Janeiro (RJ) Brazil

Modern optical interferometry has attained a high degree of precision regarding phase shift estimation, suchthat limitations stem from the quantum nature of the measurement process itself. Special quantum states oflight may beat the shot-noise limit, attained with standard light sources, leading, for lossless interferometers,to the ultimate quantum limit for the precision, the so-called Heisenberg limit. The unavoidable interactionwith the environment introduces however extra noise. An open question is what is the fundamental quantumlimit for optical interferometry in the presence of photon losses. Here we derive an analytical lower bound forthis limit, which implies, for any state of light, and even for arbitrarily small losses, that this uncertainty scalesasymptotically with the number of photons at best as the shot noise. Our bound captures the main features ofthe transition from the Heisenberg limit to the asymptotic shot-noise-like behavior.