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Deterministic teleportation of electrons in a quantum dot
nanostructure
Deics III, 28 February 2006
Richard de Visser
David DiVincenzo (IBM, Yorktown Heights)
Leo Kouwenhoven, Lieven Vandersypen (experiments, Delft)
Miriam Blaauboer
Outline
• Historic introduction to quantum entanglement
• Entanglement of electrons in solid-state systems
• Teleportation of electrons in quantum dots
• Summary
Introduction to quantum entanglement
Two particles A and B are entangled if their quantum state |ψ(AB) cannot be written as a product of two separate quantum states |ψA |ψB
• No operator
• Various measures to quantify degree of entanglement
Quantum entanglement = nonclassical correlation between (distant) particles such that manipulation of one particle instantaneously and nonlocally influences the other one
Quantum entanglement in historic context (I)
“philosophical aspects” related to foundations of quantum mechanics
EPR : quantum-mechanical systems should be local and realistic
quantum description is inconsistent with both criteria → quantum mechanics is incomplete
The Einstein-Podolsky-Rosen (EPR) paper (1935)
properties of a distant system cannot be altered instantaneously by acting on a local system
each component of quantum system characterized by its own intrinsic properties
Quantum entanglement in historic context (II)
Interlude: no further study of entanglement for thirty years
Experimental test of Bell’s inequality with photons
Aspect et al, PRL 49, 91 (1982)
confirmation that entanglement can persist over long distances → quantum mechanics is complete
1980’s
Appreciation of entanglement as a quantum resource forsending information and performing computations
... until 1964
Bell derived inequality based on EPR’slocality and realism assumptions→ can be tested experimentally
Quantum entanglement as a resource for quantum communication & quantum
computation
Pairs of entangled particles can be used to send information and perform computations in ways that are classically impossible Applications: quantum cryptography, quantum computing, teleportation, .....
Now … information is always embodied in the state of a physical system
optical(photons)
atomic(cold atoms, ions)
electronic(electrons,holes)
Three basic requirements :
1. Creation of entanglement between particles2. Coherent manipulation of entangled particles3. Detection of entanglement
Disadvantage electrons : strongly-interacting
Difficult to isolate individualentangled pairs
Short coherence times
Advantage electrons : scalability
Entanglement of electrons in solid-state systems
Idea : use electron spin pairs in quantum dots
Quantum dot = small island in a metal or semiconductor material (two-dimensional electron gas, 2DEG), confined by electrostatic gates
gates
‘artificial atom’externally controllable
Double quantum dot
‘artificial H2 molecule’
Energy spectrum of quantum dots
Single dot Single dot in magnetic field
Ground statefor two electronsis spin singlet
|↑> ↔ |0>|↓> ↔ |1>
electron-spinqubit
First challenge: creation of a nonlocal entangled
electron spin pair
Experimentally achieved by various groups
Spin singlet in double quantum dot
Adiabatic closing of interdot barrier
Electrons leave the dots
Second challenge: detection of entangled electrons
Use Bell inequality
Polarizer = electron spin rotator No experiment yet Proposal: M. B. and D. DiVincenzo, Phys. Rev. Lett. 95, 160402 (2005)
Third challenge: Coherent spin manipulations single-spin rotations and swap operations
Single spin in a quantum dot in oscillating magnetic field B1(t)
• Coherent single-spin rotation by electron spin resonance
• Swap operation: exchange of two spins
Petta et al, Science (2005)
Two spins in a double quantumdot
H(t) = J(t) S1∙ S2
Delft, 2006
Quantum teleportation
They need 3 particles : a source particle and an entangled pair
1
2 3
Alice Bob
Quantum teleportation = process whereby a quantum state is transported from one place to another without moving through intervening space
Teleportation protocol (I) Bennett et al, Phys. Rev. Lett. 70, 1895 (1993)
Alice Bob
Spin singlet
Source particle1
23
31
2 3
21
Spin singlet
Teleportation protocol (II)
Probabilistic teleportation : Alice cannot distinguish all four Bell states (“partial Bell measurements”) → teleportation with < 100 % success rate Deterministic teleportation : Alice can distinguish all four Bell states (“full Bell measurements”) → in principle 100 % success rate
Realizations of teleportation:
Probabilistic : - photons [Bouwmeester et al., 1997] - from atom to atom within the same molecule [Nielsen et al., 1998]
Deterministic : - optical fields [Furusawa et al., 1998] - ions [Riebe et al., Barrett et al., 2004]
Quantum teleportation of electrons in quantum dots
So far no teleportation experiment for electrons
Theoretical proposals : superconductors, entangled electron-hole pairs, electron-photon-electron GHZ states, electron spins in quantum dots
High level of control
Advances in coherent manipulation (rotations andexchange)
Relative robustness againstdecoherence
Goal: to design an efficient scheme for deterministic teleportation of electrons in quantum dots
Why electron spins in quantum dots?
Probabilistic teleportation scheme
25 % success rate
Alice
Bob
Towards deterministic teleportation: Alice’s Bell-state measurement
What does exist? Singlet vs. triplet (probabilistic scheme)
Measurement in standard basis
Single-shot full Bell state measurement technique for electron spins in quantum dots does not exist.
Alice’s tools: spin rotations and spin exchanges
Alice’s goal: measurement in Bell basis
Idea: transform from Bell basis to standard basis, then measure in standard basis
Brassard, Braunstein and Cleve, Physica D 120, 43 (1998)
Search for most efficient decomposition of operator USU(4),with U : maximally-entangled basis → standard basis,in terms of single-spin rotations and √swap operations
R.L. De Visser and M.B., Phys. Rev. Lett. (2006)
Result :
Total required operations for deterministic teleportation: 5 (3 single-spin rotations and 2 √swap’s)
M. Riebe et al., Nature 429, 734 (2004)
Teleportation experiment with ions
35 operations
Feasibility
When is the first electron going to be teleported?
1. Probabilistic teleportation: within 3 years (over a short distance, for example from one quantum dot to an adjacent one) → all ingredients already available
2. Deterministic teleportation: more than 5 years (but less than 10) → faster detection and spin rotations needed to avoid decoherence
My guess:
Summary
• Entanglement as fundamental property of quantum mechanics, Einstein-Podolsky-Rosen discussion
• Creation, manipulation and detection of entanglement between electrons in quantum dots
• Teleportation scheme for electrons in a quantum dot nanostructure