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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 |ψ A |ψ B 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 for sending information and performing computations... until 1964 Bell derived inequality based on EPR’s locality 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 particles 2. Coherent manipulation of entangled particles 3. Detection of entanglement Disadvantage electrons : strongly-interacting Difficult to isolate individual entangled 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 H 2 molecule’

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Energy spectrum of quantum dots Single dot Single dot in magnetic field Ground state for two electrons is spin singlet |↑> ↔ |0> |↓> ↔ |1> electron-spin qubit

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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 B 1 (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 quantum dot H(t) = J(t) S 1 ∙ S 2 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 particle 1 2 3 3 1 2 3 2 1 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 and exchange) Relative robustness against decoherence 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 U SU(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

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