1. 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

2. Outline Historic introduction to quantum entanglement Entanglement of electrons in solid-state systems Teleportation of electrons in quantum dots Summary

3. 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

4. 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

5. 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

6. 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)

7. 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

8. 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’

9. 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

10. 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

11. 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)

12. 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

13. 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

14. 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

15. 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]

16. 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?

17. Probabilistic teleportation scheme 25 % success rate Alice Bob

18. 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

19. 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)

20. 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

21. 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:

22. 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