Deterministic teleportation of electrons in a quantum dot nanostructure

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Deterministic teleportation of electrons in a
quantum dot nanostructure
Miriam Blaauboer
Richard de Visser David DiVincenzo (IBM,
Yorktown Heights) Leo Kouwenhoven, Lieven
Vandersypen (experiments, Delft)
Deics III, 28 February 2006
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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
Quantum entanglement nonclassical correlation
between (distant)
particles such that manipulation of one particle
instantaneously and
nonlocally influences the other one
Two particles A and B are entangled if their
quantum state ?(AB)? cannot be written as a
product of two separate quantum states ?A? ?B?
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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
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Quantum entanglement in historic context (II)
Interlude no further study of entanglement for
thirty years
... until 1964
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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
electronic (electrons,holes)
optical (photons)
atomic (cold atoms, ions)
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Three basic requirements 1.
Creation of entanglement between particles 2.
Coherent manipulation of entangled particles 3.
Detection of entanglement
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
artificial atom
externally controllable
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Energy spectrum of quantum dots
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First challenge creation of a nonlocal
entangled electron spin pair
Experimentally achieved by various groups
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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

• Coherent single-spin rotation by electron spin
  resonance

Single spin in a quantum dot in oscillating
magnetic field B1(t)
Delft, 2006

• Swap operation exchange of two spins

Two spins in a double quantum dot
H(t) J(t) S1 S2
Petta et al, Science (2005)
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Quantum teleportation
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)
Spin singlet
Spin singlet
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Teleportation protocol (II)

• Probabilistic teleportation Alice cannot
  distinguish all four Bell
• 
  states (partial Bell measurements) ?
• 
  teleportation with lt 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
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Probabilistic teleportation scheme
25 success rate
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Towards deterministic teleportation Alices
Bell-state measurement
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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 vswap operations
R.L. De Visser and M.B., Phys. Rev. Lett. (2006)
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Result
Teleportation experiment with ions
Total required operations for deterministic
teleportation 5 (3 single-spin rotations and 2
vswaps)
M. Riebe et al., Nature 429, 734 (2004)
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Feasibility
When is the first electron going to be teleported?
My guess

• 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
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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