On Mixed States Entanglement and Quantum Communication: Aspects of Quantum Channels Theory

• Authors: P. Horodecki
• Languages of publication: EN

Abstracts

EN

Basic aspects of quantum communication based on quantum channels theory are reviewed together with suitable examples. The key notion of quantum channel capacity is discussed. The role of mixed states entanglement as a practical tool in quantum channels theory is explained in detail. Application of recent results on non-positive partial transpose bound entanglement conjecture to binding entanglement channels shows that validity of the conjecture for some states implies nonadditivity of two-way quantum channel capacity. Some aspects of robustness of entanglement in context of positive maps theory are also discussed.

Keywords

EN

03.67.-a; 03.65.Ca; 03.67.Hk

Discipline

• 03.67.-a: Quantum information(see also 42.50.Dv Quantum state engineering and measurements; 42.50.Ex Optical implementations of quantum information processing and transfer in quantum optics)
• 03.65.Ca: Formalism
• 03.67.Hk: Quantum communication

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2002
• Volume: 101
• Issue: 3
• Pages: 399-424

Dates

published

2002-03

received

2001-06-20

Contributors

author

P. Horodecki

• Faculty of Applied Physics and Mathematics, Technical University of Gdańsk, Narutowicza 11/12, 80-952 Gdańsk, Poland

References

• 1. A. Albert, T. Beth, M. Horodecki, P. Horodecki, R. Horodecki, M. Rotteler, H. Weinfurter, R. Werner, A. Zeilinger, Quantum Information: An Introduction to Basic Concepts and Experiments, Springer-Verlag, Berlin 2001
• 2. C.H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. Smolin, W.K. Wootters, Phys. Rev. Lett., 76, 722, 1996
• 3. D. Gottesmann, I.L. Chuang, Nature, 402, 390, 1999
• 4. E. Knill, R. Laflamme, G. Milburn, http://arXive.org/abs/quant-ph/0006088
• 5. C.H. Bennett, G. Brassard, in: Proc. IEEE Conf. in Computers, Systems and Signal Processing, Bangalore (India) 1984, IEEE, New York 1984, p. 175
• 6. A. Ekert, Phys. Rev. Lett., 67, 661, 1991
• 7. P. Shor, in: Proc. 35th Annual Symp. on Foundation of Computer Science, IEEE Computer Society Press, Santa Fe, NM 1994
• 8. P. Shor, Phys. Rev. A, 52, 2439, 1995
• 9. A. Steane, Phys. Rev. Lett., 77, 793, 1996
• 10. C.H. Bennett, D.P. Di Vincenzo, J. Smolin, W.K. Wootters, Phys. Rev. A, 54, 3814, 1997
• 11. D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, A. Sanpera, Phys. Rev. Lett., 77, 2818, 1996
• 12. R.F. Werner, Phys. Rev. A, 40, 4277, 1989
• 13. P. Horodecki, Phys. Lett. A, 232, 333, 1997
• 14. V. Vedral, M. Plenio, Phys. Rev. A, 57, 1619, 1998
• 15. G. Vidal, J. Mod. Opt., 47, 355, 2000
• 16. M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. Lett., 84, 2014, 2000
• 17. M. Horodecki, Quantum Inf. Comput. J., 1, 27, 2001
• 18. M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. Lett., 80, 5239, 1998
• 19. D.P. DiVincenzo, P.W. Shor, J.A. Smolin, B. Terhal, A.W. Thapliyal, Phys. Rev. A, 61, 062312, 2000
• 20. D. Dur, J.I. Cirac, M. Lewenstein, D. Bruss, Phys. Rev. A, 61, 062313, 2000
• 21. P.W. Shor, J.A. Smolin, B.M. Terhal, Phys. Rev. Lett., 86, 2681, 2001
• 22. P. Horodecki, M. Horodecki, R. Horodecki, J. Mod. Opt., 47, 347, 2000
• 23. D. DiVincenzo, T. Mor, P. Shor, J. Smolin, B.M. Terhal, Commun. Math. Phys., in press; quant-ph/9908070
• 24. P. Horodecki, M. Horodecki, R. Horodecki, Phys. Rev. Lett., 82, 1046, 1999
• 25. B.M. Terhal, http://arXive.org/abs/quant-ph/0101032
• 26. N. Gisin, Phys. Lett. A, 210, 151, 1996
• 27. C.H. Bennett, H.J. Bernstein, S. Popescu, B. Schumacher, Phys. Rev. A, 53, 2046, 1996
• 28. D.P. DiVincenzo, P. Shor, J. Smolin, Phys. Rev. A, 57, 830, 1998
• 29. R. Alicki, private communication
• 30. P. Horodecki, R. Horodecki, Quantum Inf. Comput. J., 1, 45, 2001
• 31. S. Popescu, Phys. Rev. Lett., 72, 797, 1994
• 32. H. Barnum, E. Knill, M. Nielsen, IEEE Trans. Inf. Theory, 46, 1317, 2000
• 33. S.J. van Enk, J.I. Cirac, P. Zoller, Science, 279, 205, 1998
• 34. M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. Lett., 82, 433, 2000
• 35. B. Schumacher, M.A. Nielsen, Phys. Rev. A, 54, 2629, 1996
• 36. M. Horodecki, Ph.D. thesis, University of Gdańsk, Gdańsk 2000
• 37. A. Holevo, R. Werner, Phys. Rev. A, 63, 032312, 2001
• 38. M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. A, 60, 1888, 1999
• 39. P. Badziąg, M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. A, 62, 012311, 2000
• 40. M. Horodecki, P. Horodecki, Phys. Rev. A, 59, 4026, 1999
• 41. C. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W.K. Wootters, Phys. Rev. Lett., 70, 1895, 1993
• 42. W.H. Wootters, W.H. Zurek, Nature, 299, 802, 1982
• 43. D. Dieks, Phys. Lett. A, 92, 271, 1982
• 44. M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. Lett., 78, 574, 1997
• 45. A. Peres, Phys. Rev. Lett., 77, 1413, 1996
• 46. M. Horodecki, P. Horodecki, R. Horodecki, Phys. Lett. A, 223, 1, 1996
• 47. G. Vidal, J.I. Cirac, Phys. Rev. Lett., 80, 5803, 2001
• 48. G. Vidal, J.I. Cirac, http://arXive.org/abs/quant- ph/0107051
• 49. P. Horodecki, M. Horodecki, R. Horodecki, Acta Phys. Slovaca, 48, 141, 1998
• 50. S. Popescu, D. Rohrlich, Phys. Rev., 56, 3219, 1997
• 51. M. Horodecki, R. Horodecki, Phys. Lett. A, 244, 473, 1998
• 52. R. Horodecki, M. Horodecki, P. Horodecki, Phys. Rev. A, 63, 022310, 2001
• 53. M.D. Choi, Proc. Symp. Pure Math., 38, 583, 1982
• 54. P. Horodecki, M. Lewenstein, Phys. Rev. Lett., 1985, 2657, 2000
• 55. C.H. Bennett, D. DiVincenzo, T. Mor, P. Shor, J. Smolin, B.M. Terhal, Phys. Rev. Lett., 1982, 5385, 1999
• 56. B.M. Terhal, Lin. Algebr. Appl., 323, 61, 2000
• 57. W. Dur, J.I. Cirac, Phys. Rev. A, 61, 042314, 2000
• 58. W. Dur, J.I. Cirac, Phys. Rev. A, 62, 022302, 2000
• 59. P.W. Shor, J.A. Smolin, A.V. Thaplyial, http://arXive.org/abs/quant-ph/0005117
• 60. B. Kraus, J.I. Cirac, S. Karnas, M. Lewenstein, Phys. Rev. A, 61, 062302, 2000
• 61. A. Sanpera, R. Tarrach, G. Vidal, Phys. Rev. A, 58, 19826, 1998
• 62. M. Lewenstein, D. Bruss, J.I. Cirac, B. Kraus, M. Kuś, J. Samsonowicz, A. Sanpera, R. Tarrach, J. Mod. Opt., 47, 2481, 2000
• 63. K. Kraus, States, Effects and Operations: Fundamental Notions of Quantum Theory, Wiley, New York 1991
• 64. E. Stormer, Acta Math., 110, 233, 1963
• 65. A. Jamiołkowski, Rep. Math. Phys., 3, 275, 1972
• 66. S.L. Woronowicz, Rep. Math. Phys., 10, 165, 1976
• 67. E. Stormer, Proc. Am. Math. Soc., 86, 402, 1982
• 68. D. Bruss, J.I. Cirac, P. Horodecki, F. Hulpke, B. Kraus, M. Lewenstein, A. Sanpera, J. Mod. Opt., in press
• 69. M. Horodecki, P. Horodecki, R. Horodecki, Phys. Lett. A, 283, 1, 2001
• 70. P. Horodecki, in: Proc. NATO ARW, Mykonos (Greece) 2000, in press
• 71. P. Horodecki, unpublished
• 72. M. Ohya, D. Petz, Quantum Entropy and its Use, Springer Texts and Monographs in Physics, Springer-Verlag, Berlin 1993

Identifiers

DOI

10.12693/APhysPolA.101.399