Practical Aspects of Quantum Information Imperial College London Martin Plenio Department of Physics and Institute for Mathematical Sciences Imperial College London

Imperial College LondonImperial, 11 th 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 Rudolph Stefan Scheel Danny Terno From October 2006 Matthew Lake From October 2006 Marcus Cramer From October 2006

Imperial College LondonImperial, 11 th July 2006 QIT Methods in Many Body Physics Formal Theory of Entanglement and its Properties Application Oriented Theory Areas of Interest Implementations in: Ion traps, Cavity QED, Photonic Systems, Nano-mechanical Oscillators, Photonic Crystals Entanglement: Characterization, Manipulation, Quantification, Witnesses & Criteria Math. Found. of QM Models 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

Imperial College LondonImperial, 11 th July 2006 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 !

Imperial College LondonImperial, 11 th July 2006 Generalized Measurements Ancilla

Imperial College LondonImperial, 11 th July 2006 Generalized Measurements Apply joint unitary operation to correlate systems. Ancilla

Imperial College LondonImperial, 11 th July 2006 Generalized Measurements Projective Measurement on Ancilla:

Imperial College LondonImperial, 11 th July 2006 Generalized Measurements in Quantum Optical Systems

Imperial College LondonImperial, 11 th July 2006 Spontaneous emission: Observation of a decaying atom Initial state: State after no-click at time  t: No detection ever  Atom in ground state Each failure to detect provides information  quantum state changes!

Imperial College LondonImperial, 11 th July 2006 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 leak out of the mirrors Use no-detection events to create entanglement

Imperial College LondonImperial, 11 th July 2006 Creating entanglement in a lossy cavity

Imperial College LondonImperial, 11 th July 2006 Creating entanglement in a lossy cavity

Imperial College LondonImperial, 11 th July 2006 Now we wait and see … Creating entanglement in a lossy cavity

Imperial College LondonImperial, 11 th July 2006 No photon detected In 50% of the cases we will never see a photon  singlet state One photon detected ge eg gg ee

Imperial College LondonImperial, 11 th July 2006 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

Imperial College LondonImperial, 11 th July 2006 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)

Imperial College LondonImperial, 11 th July 2006 Generalized measurements on distant particles

Imperial College LondonImperial, 11 th July 2006 Beamsplitters make Bell projections

Imperial College LondonImperial, 11 th July 2006 Bell projection allows entanglement swapping Bell projection onto Goal: Entangle Atoms with photons Make Bell projection on photons Obtain entangled atoms

Imperial College LondonImperial, 11 th July 2006 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, (2003) Click Entangled

Imperial College LondonImperial, 11 th July 2006 Polarising Beamsplitters make Parity Check PBS Horizontal Polarization = reflected Vertical Polarization = transmitted Equally polarized photons emerge on opposite side Opposite polarized photons emerge on the same side Parity can be distinguished

Imperial College LondonImperial, 11 th July 2006 Polarization Encoding allows for Parity Measurements Murao, Plenio, Popescu, Vedral & Knight, 57, R4075 (1998) CNOT followed by measurement in computational basis is simply a parity check PBS are sufficient to implement protocol

Imperial College LondonImperial, 11 th July 2006 Many-particle Entanglement Use atoms to couple to different polarizations. Hyllus, Kieling, Schön, Eisert, Plenio, Scheel, in preparation

Imperial College LondonImperial, 11 th July 2006 Photonic Crystal Micro-cavities © Ed Hinds Quantum Dot sources: Cavity Arrays: