deterministic teleportation of electrons in a quantum dot nanostructure deics iii, 28 february 2006...
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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
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Outline
• Historic introduction to quantum entanglement
• Entanglement of electrons in solid-state systems
• Teleportation of electrons in quantum dots
• Summary
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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
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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
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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
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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)
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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
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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’
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Energy spectrum of quantum dots
Single dot Single dot in magnetic field
Ground statefor two electronsis spin singlet
|↑> ↔ |0>|↓> ↔ |1>
electron-spinqubit
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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
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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)
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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
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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
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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
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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]
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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?
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Probabilistic teleportation scheme
25 % success rate
Alice
Bob
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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
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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)
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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
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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:
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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