Quantum correlations and secret bits

Physical Review Letters

Volumn 94, Issue 2, 2005, Pages

  Acín, Antonio ^a   Gisin, Nicolas ^b  

^a ICFO INSTITUT DE CIENCIES FOTONIQUES   (Spain)

^b UNIVERSITY OF GENEVA   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR COMBINATIONS; QUANTUM CORRELATIONS; QUANTUM RESOURCES; QUANTUM SYSTEMS;

COMMUNICATION SYSTEMS; INFORMATION THEORY; NETWORK PROTOCOLS; PROBABILITY DISTRIBUTIONS; QUANTUM CRYPTOGRAPHY;

QUANTUM THEORY;

EID: 18144378105     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.94.020501     Document Type: Article

References (27)

1. B. M. Terhal, IBM J. Res. Dev. 48, 71 (2004).
2. A. Ekert, Phys. Rev. Lett. 67, 661 (1991).
3. J. S. Bell, Physics 1, 195 (1964).
4. P. W. Shor and J. Preskill, Phys. Rev. Lett. 85, 441 (2000).
5. C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India (IEEE, New York, 1984), pp. 175-179.
6. N. Gisin and S. Wolf, in Proceedings of CRYPTO 2000, Lecture Notes in Computer Science Vol. 1880 (Springer-Verlag, Berlin, 2000), p. 482.
7. D. Collins and S. Popescu, Phys. Rev. A 65, 032321 (2002).
8. A. Acín, Ll. Masanes, and N. Gisin, Phys. Rev. Lett. 91, 167901 (2003).
9. I. Devetak and A. Winter, Phys. Rev. Lett. 93, 080501 (2004).
10. K. Horodecki, M. Horodecki, P. Horodecki, and J. Oppenheim, quant-ph/0309110.
11. R. Renner and S. Wolf, in Proceedings of Advances in Cryptology - EUROCRYPT 2003: International Conference on the Theory and Applications of Cryptographic Techniques, Warsaw, Poland, 2003, Lecture Notes in Computer Science (Springer-Verlag, Berlin, 2003).
12. Whether these secret correlations can be extracted or distilled into perfect secret bits, a key is a different, though related, problem that we do not consider here.
13. P. M. Hayden, M. Horodecki, and B. M. Terhal, J. Phys. A 34, 6891 (2001).
14. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 54, 3824 (1996).
15. R. F. Werner, Phys. Rev. A 40, 4277 (1989).
16. U. Maurer and S. Wolf, IEEE Trans. Inf. Theory 45, 499 (1999).
17. L. P. Hughston, R. Josza, and W. K. Wootters, Phys. Lett. A 183, 14 (1993).
18. M. Curty, M. Lewenstein, and N. Liitkenhaus, Phys. Rev. Lett. 92, 217903 (2004).
19. Note that the classical postprocessing, P(Z̄|Z), can always be included in Eve's measurement.
20. M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki, Phys. Rev. A 62, 052310 (2000).
21. O. Guehne et al., J. Mod. Opt. 50, 1079 (2003).
22. C. H. Bennett, G. Brassard, and N. D. Mermin, Phys. Rev. Lett. 68, 557 (1992).
23. Both possibilities can be true since (i) one can derive many probability distribution containing secret correlations from any bound entangled state, and (ii) bound information could be proven for probability distributions not associated with quantum states.
24. The existence of bound information in a multipartite scenario has been shown in A. Acín, J. I. Cirac, and Ll. Masanes, Phys. Rev. Lett. 92, 107903 (2004). The proof for the case of two honest parties still remains elusive.
25. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. A 60, 1888 (1999).
26. H. F. Hofmann, Phys. Rev. A 68, 034307 (2003); O. Gühne, Phys. Rev. Lett. 92, 117903 (2004).
27. H. F. Hofmann, Phys. Rev. A 68, 034307 (2003); O. Gühne, Phys. Rev. Lett. 92, 117903 (2004).