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. 2 Outline Introduction to W states Generation schemes Robustness Applications

3. 3 Introduction to W states

4. 4 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 Са 40. F.Schmidt-Kaler et al Science, 304, 1478, (2004). Decoherence-free communications. H.Weinfurter et al PRL, 92, 107901 (2004). |0>, |1> are logical states 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). Multiparticle entangled states

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

6. 6 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) Connection with Dicke states

7. 7 … where is the antisymmetric Bell state. The Young scheme [n-1 n] 1 2 3kn1 3 2 k n 1 k 23n1 n 23k ++ + If Collective evolution of n particles reduces to evolution of n-2 particles. A representation … … …… +

8. 8 Generation schemes

9. 9 Optical experiment by H.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) Generation

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

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

12. 12 1 Biphoton Bs Detector Transformation of the Fock state The state of biphoton Rate of generation. A pulsed-pumped laser with pulse 100 fs and 100 MGH repetition rate, average power of 200 mW,, a pair per 10 4 pulses, the generation rate of biphoton or desired state Is about 10 4 per second. In experiment of generation of polarized W the rate was about 1 per minute. Optical scheme on biphotons

13. 13 Robustness

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

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

16. 16 1. Dispersive limit 2. Bath is in vacuum state 3. Non-collective relaxation is neglected Approximations Master equation for atomic density matrix Exact solution for the density matrix where Master equation for atoms

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

18. 18 The two-particle non-local operator converts three - particle GHZ state into W Connection with GHZ states

19. 19 Applications

20. 20 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) Applications

21. 21 Thank you