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Multiparticle Entangled States of the W- class, their Properties and Applications

Multiparticle Entangled States of the W- class, their Properties and Applications. A. Rodichkina , A. Basharov, V. Gorbachev Laboratory for Quantum Information & Computation, AeroSpace University, St.-Petersburg 190000, Bolshaia Morskaia 67, Russia ,

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Multiparticle Entangled States of the W- class, their Properties and Applications

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  1. Multiparticle Entangled States of the W- class, their Properties and Applications A. Rodichkina, A. Basharov, V. Gorbachev Laboratory for Quantum Information & Computation, AeroSpace University, St.-Petersburg 190000, Bolshaia Morskaia 67,Russia, Laboratory for nonlinear optics, RRC "Kurchatov Institute", Moscow 123182, Russia. Supported by Delzell Foundation Inc. and RFBR grant 06-02-16769.

  2. Outline • Introduction to W states • Generation schemes • Robustness • Applications

  3. Introduction to W states

  4. Multiparticle entangled states |0>, |1> are logical states • Two level atom • Polarized light |H>, |V> • Fock states of light |n>, with n=1,0 photons. • Experiment • Polarized photons. H.Weinfurter et al PRL, 92, 087902 and 077901 (2004) . • Ions Са40. F.Schmidt-Kaler et al Science, 304, 1478, (2004). • Decoherence-free communications. H.Weinfurter et al PRL, 92, 107901 (2004). Reviews on W states A. Karlsson, M. Bourennane et al. Quant. Computer and Computing, 4, 3, (2003) . V.N. Gorbachev, A.I. Trubilko. Laser Phys. Lett. 3, No. 2, 59-70 (2006).

  5. Dicke states • Dicke states are specified by three quantum numbers j,m,a. where k=1,2,3 |m| j,j=o,.. n-1, n is number of particles, quantum number a describes degeneracy, it takes values. R. Dicke. Phys. Rev. 93, 99, 1954. • For two level atoms where are Pauli matrices of the m-th atom

  6. Connection with Dicke states • These states are also known as Zero Sum Amplitude states • (A.K. Pati. J. Physics, 59, 217 (2002)). (V.N. Gorbachev, A.I. Trubilko, JETP, 101, 33, 2005)

  7. A representation • If is the antisymmetric Bell state. where … • The Young scheme [n-1 n] + + 1 3 k n 1 2 n … … k 2 3 1 2 3 n + 1 2 3 k + … … k n • Collective evolution of n particles reduces to evolution of n-2 particles.

  8. Generation schemes

  9. Generation Optical experiment byH.Weinfurter et al PRL, 92, 087902 and 077901 (2004) • Input 4-photon state • The three-polarized photon state is prepared with probability 1/36 (after post selection)

  10. Generation - 2 • Qubits are encoded in the ground and metastable states D and S Experiment with trapped ions 40 Ca+byF.Schmidt-Kaler et al. Science, 304, 1478, (2004) D • Laser pulse can rotate each ion R S • Each ion interacts with a vibration mode • Operations R and R+ have been implemented experimentally.

  11. Schemes for generation of atomic states • Atomic W states n atoms detector • W states from atomic ensembles V. Gorbachev et al Phys.Lett. A, 310, 339, 2003 .

  12. Optical scheme on biphotons • Transformation of the Fock state Detector 1 Biphoton • The state of biphoton Bs • Rate of generation. A pulsed-pumped laser with pulse 100 fs and 100 MGH • repetition rate, average power of 200 mW, , a pair per 104 pulses, the generation • rate of biphoton or desired state Is about 104 per second. In experiment of generation • of polarized W the rate was about 1 per minute.

  13. Robustness

  14. Robustness • Robustness to loss of particle. "Persistency of entanglement”,Briegel et.al. Phys. Rev. Lett., 86, 910, (2001) • Immunity to collective interactions. : is annihilated by the collective operator if • Application for storage of quantum states. (A. Basharov et al PRA, 2006) • Let a physical process be described by the equation where then the state Is conserved:

  15. Collective decay of atoms • Tavis-Cummings model M F A Broad band field or bath Two-level atoms Cavity mode • Hamiltonian where • Master Equation for atoms • The presented model describes impurities in nanocrystal (A. Basharov et al. Russian Quant Electronics, 2006)

  16. Master equation for atoms • Approximations • Dispersive limit • Bath is in vacuum state • Non-collective relaxation is neglected • Master equation for atomic density matrix • Exact solution for the density matrix where

  17. Storage of entangled states then = Const(t) and it has immunity to decay • If • In contrast atoms in the cavity • Scheme for writing and storing photon BS • Swapping: Swapping photon-atoms: V. Gorbachev et al. Phys. Lett. A, Vol 323/5-6, 339, (2004)

  18. Applications

  19. Applications • Using W states in the standard protocols Conditional teleportation (B.-S. Shi, A Tomita. Phys.Lett. A, 296, 161, (2002), J.Joo, Y.J. Park, S.Oh, J.Kim. New Journal of Phys. 5, 136, (2003) Unconditional teleportation of entangled states, three-qubit dense coding (V. Gorbachev et al Phys. Lett. A 314, 267, (2003)) and Quantum key distribution. (J. Joo,J. Lee, J. Jang, Y.-J Park. E-print, LANL, quant-ph/0204003 (2002)) • Application due to features of W states Collective decay and storage of quantum states in collective thermostat. (A. Basharov et. al. PRA, (2006) in print)

  20. Thank you 

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