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