practical aspects of quantum information imperial college london martin plenio department of physics...
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Practical Aspects of Quantum Information
Imperial College London
Martin PlenioDepartment of Physics
and
Institute for Mathematical Sciences
Imperial College Londonwww.imperial.ac.uk/quantuminformation
Imperial College London Imperial, 11th July 2006
The IMS Team
Martin Plenio, Programme Leader
Jens Eisert, EurYI fellow
Shashank Virmani
Postdocs:
Moritz Reuter
PhD students:
Koenraad Audenaert
Christopher Dawson
Michael Hartmann
Philip Hyllus
Kenneth Pregnell
Alexander Retzker
Alessio Serafini
Fernando Brandão
Oscar Dahlsten
Alvaro Feito
David Gross
Konrad Kieling
+ Affiliated Groups of: Peter Knight Terry RudolphStefan Scheel
Danny TernoFrom October 2006
Matthew LakeFrom October 2006
Marcus CramerFrom October 2006
Imperial College London Imperial, 11th July 2006
QIT Methods in Many Body Physics
Formal Theory of Entanglement and its
Properties
Application OrientedTheory
Areas of Interest
Implementations in: Ion traps, Cavity QED, Photonic Systems, Nano-mechanical Oscillators, Photonic Crystals
Entanglement: Characterization, Manipulation, Quantification, Witnesses & CriteriaMath. Found. of QMModels of Computation
Apply QIT to: Scaling Laws, Simulation Methods, Dynamics, Critical Systems, Emulating Hamiltonians, Geometric Phases
Concepts: Linear Optics Quantum Computation, Manipulation by Propagation, Entanglement Generation by Measurement
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Projective Measurements
Projective Measurement
That’s what you learned in your quantum mechanics course!
… and we cannot be more general than that !?
Yes and No !
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Generalized Measurements
Apply joint unitary operationto correlate systems.
Ancilla
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Generalized Measurements
Projective Measurement on Ancilla:
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Generalized Measurements in Quantum Optical Systems
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Spontaneous emission: Observation of a decaying atom
Initial state:
eg eeg t
State after no-click at time t:
No detection ever Atom in ground state
g
Each failure to detect provides information quantum state changes!
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Ingredients:• Spontaneous decay• Interaction between atoms
Idea: take two atoms in an optical cavity
Symmetrical positions
M.B. Plenio, S.F. Huelga, A. Beige, P.L. Knight, Phys. Rev. A 59, 2468 (1999)
Photons may leakout of the mirrors
Use no-detection events to create entanglement
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Now we wait and see …
Creating entanglement in a lossy cavity
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No photon detected
)22
(2
1 vac
geegvac
geeg
vacegini
In 50% of the cases we will never see a photon singlet state
vacgeeg
ini
2
One photon detected
photonggini
ge eg
gg
ee
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Imperfect detector registers ‘no-click’
• No photon has leaked out of the cavity
• A photon has left the cavity but has been missed by the detector
Resulting partially entangled state is of the form:
Detector efficiency = p
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Many photons will be emitted
No photons will be emitted
Detector will see some photons after sufficiently long time
When no photons are seen, success prob = p
M.B. Plenio, S.F. Huelga, A. Beige, P.L. Knight, Phys. Rev. A 59, 2468 (1999)
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dcbaba vaccvacba 01)(
2
1
2
0110
dcbaba vacdvacba 10)(
2
1
2
0110
Beamsplitters make Bell projections
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Bell projection allows entanglement swapping
Bell projectiononto
Goal: Entangle Atoms with photons Make Bell projection on photons
Obtain entangled atoms
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S. Bose, P.L. Knight, M.B. Plenio and V. Vedral, PRL 58, 5158 (1999)D.E. Browne, M.B. Plenio, and S.F. Huelga, PRL 91, 067901 (2003)
Click
Entangled
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Polarising Beamsplitters make Parity Check
PBS
Horizontal Polarization = reflectedVertical Polarization = transmitted
Equally polarized photons emerge on opposite sideOpposite polarized photons emerge on the same side
Parity can be distinguished
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Polarization Encoding allows for Parity Measurements
Murao, Plenio, Popescu, Vedral & Knight, 57, R4075 (1998)
CNOT followed by measurement in computational basis is simplya parity check
PBS are sufficient to implement protocol
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Many-particle Entanglement
Use atoms to couple todifferent polarizations.
Hyllus, Kieling, Schön, Eisert, Plenio, Scheel, in preparation