Introduction Past Projects Future Projects
Polarization and frequency entanglement forexperiments in
bulk and integrated optics
Alvaro Andres Cuevas Seguel
Physics Department, Sapienza University of Rome,Piazzale Aldo Moro 5, I-00185 Roma, Italy
January 27, 2016
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Outline
1 Introduction
2 Past Projects
3 Future Projects
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Entanglement
Entanglement with Light
The quantum binary information element is the Qubit |ψ〉 = α |1〉+ β |2〉Imagine two coupled systems represented by their own qubits.
Separable State (SS): The bipartite Hilbert space can be written as tensorproduct of both density matrices ρ = |ψ〉 〈ψ|.Entangled State (ES): Opposite to the SS, e.g. ρ1,2 6= ρ1 ⊗ ρ2.
Polarization Entanglement (PE): Encodes qubits in the light polarization basis.
|ψ〉 = α |H〉1 |V 〉2 + β |V 〉1 |H〉2 (1)
Polarization-Frequency Entanglement (PFE): Like PE, but adding distinguishedlight wavelengths to each polarization mode.
|ψ〉 = α |H〉λ1|V 〉λ2
+ β |V 〉λ1|H〉λ2
(2)
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Optical Source of Entanglement
Spontaneus Parametric Down Conversion (SPDC)
Type-II SPDC
A pumping photon excites a valence electron of a non-linear crystal.
When the electron decays two photons emerge, but with new wavelengths.
The process conserve energy ωp = ωs + ωi and momentum kp = ks + ki
Ordinary polarized pump generates photons with orthogonal polarizations(ordinary and extraordinary).
Quasi-Phase-Matching in Periodic Poled KTP compound
Periodically alternate non-linear index
Keeps only the positive phase contributes of the SPDC along the crystal.
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Optical Source of Entanglement
Sagnac Source of Entangled Photons
Compensates optical paths phase difference between the clockwise andanti-clockwise beams.
Pump power-polarization control
Double SPDC for the generation indistinguishability and entanglement.
Active oven for the temperature control, and inclination control for thecollinearity.
Tomography stages and customizable focalization.
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Source Optimization
Improving the entanglement source quality
Changes
Singlemode laser
PM optical fiber
Spatial filter by pinhole
Erasure of diffraction rings
Crystal focalization
Interference filters of FWHM = ±3[nm]
Telescope optimization
Pumping at 2, 5[mW ] Concurrence [%] Fidelity [%] Single. C. [ 1s
] Coin. C.[ 1s
] Spec. Band [nm]
Old Source 96,5 95 46900 4600 5New Source 98 98,5 337500 61500 0,5
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Open Systems
Non-Markovian Dynamics
Sequence of two system-environment interactions
Loss of original information (entanglement with an ancilla)
Backflow of information or Non-Markovian (NM) dynamics.
NM: non positive or completely positive decomposition of a system evolutionoperator.
WNM: non completely positive decomposition of a system evolution operator.
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Open Systems
Results
Identification of a ”‘Weak Non-Markovianity”’ (WNM), unseen by thetraditional information backflow techniques.
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Amendable Channels
Amending Entanglement Breaking Maps (EBM)
An EBMn, applied n-times destroy the entanglement between a sample systemand an ancilla.
Suppose a map Ψs ∈ EBM2 composed by a Half Wave Plate (HWP) after anAmplitude Damping Channel.
Suppose a map Φs ∈ EBM2 composed by an ADP after a HWP.
Then, Ψs ◦Ψs(ρs,a), Φs ◦ Φs(ρs,a) and Φs ◦ Φs ◦Ψs ◦Ψs(ρs,a) destroyentanglement.
Amendable Channel by Filter Map
Ψs ◦Θs ◦Ψs(ρs,a) /∈ EBM2
Where Θs is the Filter map composed by two consecutive HWPs.
Amendable Channel by Cut & Paste Map
Φs ◦Ψs ◦ Φs ◦Ψs(ρs,a) /∈ EBM2
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Amendable Channels
Amplitude Damping Channel (ADC)
α |H〉 −→ α |H〉 (3)
β |V 〉 −→ β(√η |V 〉+
√1− ηα |H〉)
E1 =
(1 00√η
)and E2 =
(0√
1− η0 0
)(4)
Filtered Channel Scheme
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Amendable Channels
Cut And Paste Channel Scheme
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Quantum Channel Capacity
Lower bounds to the Quantum Channel Capacity (Q)
In noisy quantum communication channels
Q > QDetectable = S
(ε
(I
d
))− H(~p) (5)
S(ρ) = −Tr [ρlog2(ρ)] is the Von Neumann Entropy
H(x) = −xlog2(x)− (1− x)log2(1− x) is the ShannonEntropy
ε(ρ) =∑
j AjρA†j is the noisy channel operator.
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Quantum Channel Capacity
H must be minimized by some optimized parameters,
One has to measure σsx ⊗ σax , σsy ⊗ σay and σsz ⊗ σazA considerable reduction in the number of measurementscompared with a tomography.
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Quantum Walks in Integrated Photonics
Super-diffusion of Photons in randomly diluted QuantumWalks (QW)
In a network of Mach-Zehnder (MZ) interferometers, whereeach step is considered as an integrated QW, transmittedinput photons choose sequentially which output to take.
The length differences between MZ’s arms is equivalent to aphase difference.
Ordered QW: For any step the MZ’s phase differences arezero, transporting geometrically diffused light.
Static Disordered QW: For any step the phases present astatistical static disorder, transporting non diffusive light.
Anderson Localization
Evolving Disordered QW: New effect of super-diffusion.
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Quantum Walks in Integrated Photonics
Known Diffusion or Anderson Localization for Single Photons
Known Diffusion or Anderson Localization for Entangled Photons
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Generalized non-Markovianity
Generalized Trace Distance Criterion
A quantum process Φ is defined to be Markovian if the Trace Distance (TD)between two biased mapped states
||p1Φt(ρ1)− p2Φt(ρ2)||1 = Tr |p1Φt(ρ1)− p2Φt(ρ2)| (6)
decrease with t ≥ 0.
We define Iint = ||p1Φ1S (t)− p2Φ2
S (t)||1 and Iext = ||p1Φ1S (t)− p2Φ2
S (t)||1correlated by the information relation Iint(t) + Iext(t) = Iint(0) = cons
Quantifying the degree of memory effects by continuity in t we get a new TD
N(Φ) = max{pi}, ρ2 ∈ ∂U(ρ1)
∫σ>0
dtσ(t, piρi ) (7)
Where σ(t, pi , ρi ) ≡ 1||p1ρ1−p2ρ2||1
1dt||p1Φt(ρ1)− p2Φt(ρ2)||1.
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Generalized non-Markovianity
P-divisibility is no more enough to prove Markovianity, weneed to use also CP-divisibility.
The idea of the work is to measure the generalized tracedistance of two states before and after some map.
If the TD weights are p1 = p2 we are not abble to detectnon-Markovianity.
It the TD weights are p1 6= p2 (under some restrictions) weare able to detect non-Markovianity.
Confirmation of a local and universal representation of themeasure of Markovianity.
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Generalized non-Markovianity
Thank you for your attention!!!
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