Distillation protocols: Output entanglement and local mutual information

Physical Review Letters

Volumn 93, Issue 17, 2004, Pages

  Horodecki, Michal ^a   Oppenheim, Jonathan ^a,b   Sende, Aditi ^c   Sen, Ujjwal ^c  

^a UNIVERSITY OF GDA SK   (Poland)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^c LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINT THEORY; DISTILLATION; ENTROPY; ERROR ANALYSIS; INFORMATION THEORY; MATHEMATICAL OPERATORS; PROBABILITY DISTRIBUTIONS; QUANTUM THEORY;

ARBITARY BIPARTITE ENSEMBLES; BELL-DIAGNOL STATES; DISTILLATION PROTOCOLS; LOCAL MUTUAL INFORMATION;

NETWORK PROTOCOLS;

EID: 19744382502     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.93.170503     Document Type: Article

References (32)

1. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, Phys. Rev. Lett. 76, 722 (1996).
2. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 54, 3824 (1996).
3. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
4. K.G.H. Vollbrecht and M. M. Wolf, Phys. Rev. A 67, 012303 (2003).
5. J. Walgate, A. J. Short, L. Hardy, and V. Vedral, Phys. Rev. Lett. 85, 4972 (2000);
6. S. Virmani, M. F. Sacchi, M. B. Plenio, and D. Markham, Phys. Lett. A 288, 62 (2001); Y.-X. Chen and D. Yang, Phys. Rev. A 64, 064303 (2001); 65, 022320 (2002).
7. S. Virmani, M. F. Sacchi, M. B. Plenio, and D. Markham, Phys. Lett. A 288, 62 (2001); Y.-X. Chen and D. Yang, Phys. Rev. A 64, 064303 (2001); 65, 022320 (2002).
8. S. Virmani, M. F. Sacchi, M. B. Plenio, and D. Markham, Phys. Lett. A 288, 62 (2001); Y.-X. Chen and D. Yang, Phys. Rev. A 64, 064303 (2001); 65, 022320 (2002).
9. Henceforth, by "distinguishing", we will mean "local distinguishing".
10. J. P. Gordon, in Proceedings of the International School of Physics "Enrico Fermi, Course XXXI", edited by P. A. Miles (Academic Press, NY, 1964), p. 156; L. B. Levitin, in Proceedings VI National Conference Information Theory, Tashkent (1969), p. 111; A.S. Holevo, Prob. Peredachi Inf. 9, 3 1973 [ Problems of Information Transmission (Engl Trans) 9, 110 (1973)].
11. J. P. Gordon, in Proceedings of the International School of Physics "Enrico Fermi, Course XXXI", edited by P. A. Miles (Academic Press, NY, 1964), p. 156; L. B. Levitin, in Proceedings VI National Conference Information Theory, Tashkent (1969), p. 111; A.S. Holevo, Prob. Peredachi Inf. 9, 3 1973 [ Problems of Information Transmission (Engl Trans) 9, 110 (1973)].
12. J. P. Gordon, in Proceedings of the International School of Physics "Enrico Fermi, Course XXXI", edited by P. A. Miles (Academic Press, NY, 1964), p. 156; L. B. Levitin, in Proceedings VI National Conference Information Theory, Tashkent (1969), p. 111; A.S. Holevo, Prob. Peredachi Inf. 9, 3 1973 [ Problems of Information Transmission (Engl Trans) 9, 110 (1973)].
13. J. P. Gordon, in Proceedings of the International School of Physics "Enrico Fermi, Course XXXI", edited by P. A. Miles (Academic Press, NY, 1964), p. 156; L. B. Levitin, in Proceedings VI National Conference Information Theory, Tashkent (1969), p. 111; A.S. Holevo, Prob. Peredachi Inf. 9, 3 1973 [ Problems of Information Transmission (Engl Trans) 9, 110 (1973)].
14. B. Schumacher, M. Westmoreland, and W. K. Wootters, Phys. Rev. Lett. 76, 3452 (1996).
15. P. Badziag, M. Horodecki, A. Sen(De), and U. Sen, Phys. Rev. Lett. 91, 117901 (2003).
16. The results obtained are independent of whether it was Alice or Bob who started the protocol.
17. T. M. Cover and J. A. Thomas, Elements of Information Theory, (Wiley, New York, 1991).
18. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 84, 2014 (2000); See also M. Donald, M. Horodecki, and O. Rudolph, J. Math. Phys. (N.Y.) 43, 4252 (2002).
19. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 84, 2014 (2000); See also M. Donald, M. Horodecki, and O. Rudolph, J. Math. Phys. (N.Y.) 43, 4252 (2002).
20. M. Horodecki, Quantum Inf. Comput. 1, 3 (2001).
21. 2). This inequality essentially says that forgetting of information is not useful to increase entanglement. If this inequality does not hold for some choice of the density matrices (and probabilities), then the corresponding entanglement measure is said to be nonconvex.
22. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 80, 5239 (1998); P. Horodecki, Phys. Lett. A 232, 333 (1997).
23. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 80, 5239 (1998); P. Horodecki, Phys. Lett. A 232, 333 (1997).
24. P. W. Shor, J. A. Smolin, and B. M. Terhal, Phys. Rev. Lett. 86, 2681 (2001).
25. D.P. DiVincenzo, P.W. Shor, J.A. Smolin, B.M. Terhal, and A.V. Thapliyal, Phys. Rev. A 61, 062312 (2000); W. Dur, J. I. Cirac, M. Lewenstein, and D. Bruss, Phys. Rev. A 61, 062313 (2000).
26. D.P. DiVincenzo, P.W. Shor, J.A. Smolin, B.M. Terhal, and A.V. Thapliyal, Phys. Rev. A 61, 062312 (2000); W. Dur, J. I. Cirac, M. Lewenstein, and D. Bruss, Phys. Rev. A 61, 062313 (2000).
27. A. Peres, Phys. Rev. Lett. 77, 1413 (1996); M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A 223, 1 (1996).
28. A. Peres, Phys. Rev. Lett. 77, 1413 (1996); M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A 223, 1 (1996).
29. C. H. Bennett, H. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A 53, 2046 (1996).
30. 2πijn/d|j〉|(j + m)mod d〈 (n, m = 0,..., d - 1). For d = 2, it is the familiar Bell basis.
31. P.W. Shor and J. A. Smolin, quant-ph/9604006.
32. S. Ghosh, P. Joag, G. Kar, S. Kunkri, and A. Roy, quant-ph/0403134.