2. Quantum Entanglement and Distillation in Information Processing Shao-Ming Fei 2011.04.18

3. Quantum Entanglement Pure state: v ector on Separable! bipartitetripartite multipartite

4. a) PPT criterion: Separability: no general criteria b) Reduction: Mixed state: density matrix Separable! Realignment, Covariance matrix criterion, …

5. Measure: Bipartite Entanglement of Formation (EoF) Pure state

6. Measurable bounds for EoF M. Li, S.M. Fei, Phys. Rev. A 82 (2010) 044303 Lower Bound for EoF K. Chen, S. Albeverio, S.M. Fei, Phys. Rev. Lett. 95(2005)210501 S.M. Fei, X. Li-Jost, Phys. Rev. A 73(2006)024302 Mixed state

7. Relative Entropy, Negativity, …….. Lower Bound for Concurrence K. Chen, S. Albeverio, S.M. Fei, Phys. Rev. Lett. 95(2005)040504 X.H. Gao, S.M. Fei and K. Wu, Phys. Rev. A 74 (Rapid Comm.)(2006)050303 M. Li, S.M. Fei and Z.X. Wang, J. Phys. A 42 (2009) 145303 X.S. Li, X.H. Gao and S.M. Fei, Phys. Rev. A 83 (2011) 034303 Concurrence

8. Two-qubit: A. Buchleitner et.al. Nature 440(2006)1022 Experimental measurement of entanglement

9. Three qubits Two qubits Theorem (multi-qubit):

10. S.M. Fei, M.J. Zhao, K. Chen and Z.X. Wang, Phys. Rev. A 80 (2009) 032320 N-partite M-dimensional case: SU(M) generators

11. Entanglement as resource in quantum formation processing Quantum computation Quantum teleportation Dense coding Quantum cryptography Quantum error correction Quantum repeater Phase transition

12. 1 qubit2 bit1 qubit AliceBob Entanglement enhanced

13. AliceBob Entanglement enhanced

14. 1 qubit AliceBob 2 bit Entanglement enhanced

15. 1 qubit2 bit1 qubit AliceBob Entanglement enhanced

16. Optimal Teleportation M. Li, S.M. Fei and Z.X. Wang, Phys. Rev. A 8 (2008) 032332 M.J. Zhao, Z.G. Li, S.M. Fei and Z.X. Wang, J. Phys. A 43, (2010) 275203 Fully entangled fraction: M. Horodecki, P. Horodecki and R. Horodecki, Phys. Rev. A 60, 1888 (1999) S. Albeverio, S.M. Fei, Phys. Lett. A 276(2000)8 S. Albeverio, S.M. Fei and W.L. Yang, Phys. Rev. A 66 (2002) 012301

17. $ ~ ? Bipartite system with one subsystem undergoes a noisy channel Evolution of quantum entanglement: Z.G. Li, S.M. Fei, Z.D. Wang and W.M. Liu, Phys. Rev. A,79 (2009) 024303 Two-qubit: Buchleitner et. al., Nature Physics 4, 99 (2008)

18. Kraus operator E.g. generalized amplitude damping channel

19. Atom-Cavity System zero detuning Evolution of quantum entanglement: (Hamiltonian ~ master equation) J.H. Eberly and T. Yu, Science 316 (2007) 555

20. L.L. Lan, X.B. Wang and S.M. Fei, Int. J. Quant. Inform. 8 (2010)1239

21. Entanglement of Assistance (EoA) A B C Z.G. Li, S.M. Fei, S. Albeverio, W.M. Liu, Phys. Rev. A 80 (2009) 034301 Evolution of EoA Z.G. Li, M.J. Zhao, S.M. Fei and W. M. Liu, Phys. Rev. A 81 (2010) 042312

22. Distillation: U U Entangled, but not distillable: bound entangled Measurement

23. Separable PPT (positive partial transpose) All PPT entangled states are bound entangled! Non PPT distillable ? no answer yet Violation of reduction criterion distillable Distillability from Bell inequalities

25. M. Li, S.M. Fei, Phys. Rev. Lett. 104 (2010) 240502

26. Improving capacity of noisy channels 12 max. entangled $ 21 bound entangled 12 43 21 43 $

27. bound entangled!

28. on 1 and 3 by Alice Alice measures 1 Bob measures 2 => |0> Maximally Entangled !

29. Quantum Discord (quantum correlation besides entanglement) Quantum mutual information project measurement performed on subsystem B Quantum conditional entropy Associated quantum mutual information Classical correlation Quantum discord S. Luo, Phys. Rev. A 77 (2008) 042303

31. Undergoes the phase flip channel Concurrence (dashed line) and quantum discord (solid line) under phase flip channel for B. Li, Z.X. Wang, S.M. Fei, Phys. Rev. A 83 (2011) 022321

33. H. Dong, D. Z. Xu, C. P. Sun, Coherent excitation transferring via dark state in light-harvesting process, arXiv:1102.0960 Entanglement in Biological structure