Information-theoretic aspects of inseparability of mixed states

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 54, Issue 3, 1996, Pages 1838-1843

  Horodecki, Ryszard ^a   Horodecki, MichalØ ^a  

^a UNIVERSITY OF GDA SK   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001339646     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.54.1838     Document Type: Article

References (32)

1. K. Blum, Density Matrix Theory and Applications (Plenum, New York, 1981).
2. B. d'Espagnat Conceptual Foundations of Quantum Mechanics (Benjamin, Reading, MA, 1976).
3. A. Einstein, B. Podolsky and N. Rosen, Phys. Rev. 47, 777 (1935).
4. E. Schrödinger, Naturwissenschaften 23, 807 (1935).
5. S. Bell, Physics (NY) 1, 195 (1964).
6. The term ``nonlocality'' is slightly misleading, as in fact one deals with violation of the conjunction of the two conditions: locality and objectivism. However, with respect to common tradition, we will use further the term ``locality'' (``nonlocality'') related to satisfying (violating) the assumptions of local realism, respectively.
7. L. Braunstein and C. M. Caves, Phys. Rev. Lett. 61, 662 (1988).
8. B. W. Schumacher, Phys. Rev. A 44, 7047 (1991).
9. K. Wódkiewicz, Phys. Rev. A 52, 3501 (1995).
10. S. M. Barnett and S. J. D. Phoenix, Phys. Rev. A 44, 535 (1991).
11. R. Horodecki, Phys. Lett. A 187, 145 (1994).
12. R. Horodecki and P. Horodecki, Phys. Lett. A 194, 147 (1994).
13. R. Horodecki, P. Horodecki and M. Horodecki, Phys. Lett. A 210, 377 (1996).
14. C. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
15. S. Popescu, Phys. Rev. Lett. 72, 797 (1994).
16. see, in this context, N. Gisin, Phys. Lett. A 210, 157 (1996).
17. S. Massar and S. Popescu, Phys. Rev. Lett. 74, 1259 (1995).
18. By standard teleportation scheme we mean here that Alice uses Bell basis in her measurement while Bob is allowed to apply any unitary transformations.
19. R. Horodecki, M. Horodecki, and P. Horodecki (unpublished).
20. W. Thirring, Vorlesungen über mathematische Physik (University of Vienna, Vienna, 1975).
21. A. Wehrl, Rep. Mat. Phys. 10, 159 (1976).
22. See e.g., Ch. Beck and D. Graudenz, Phys. Rev. A 46, 6265 (1992).
23. By the classical discrete states we mean here joint probability distributions defined on product probability space (Formula presented)×(Formula presented) where (Formula presented).
24. R. F. Werner, Phys. Rev. A 40, 4277 (1989).
25. W. Thirring, Lehrbuch der Mathematischen Physik (Springer-Verlag, Wien, 1980).
26. R. Horodecki and P. Horodecki, Phys. Lett. A 210, 227 (1996).
27. The considered line represents mixtures of singlet states and the identity. The mixtures belong to the family of the states introduced by Werner 22 and they have been considered in the context of teleportation in Ref. 14.
28. Omitted end note.
29. N. J. Cerf and C. Adami, Report No. quant-ph/9512022 (unpublished).
30. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. Smolin and W. K. Wootters, Phys. Rev. Lett. 76, 722 (1996).
31. S. Popescu, Phys. Rev. Lett. 74, 2619 (1995).
32. N. Gisin, Phys. Lett. A 210, 151 (1996).