Unified criterion for security of secret sharing in terms of violation of Bell inequalities

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 68, Issue 3, 2003, Pages 032309/1-032309/7

  Sen De, Aditi ^a   Sen, Ujjwal ^a   żukowski, Marek ^a  

^a UNIVERSITY OF GDA SK   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242610895     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.68.032309     Document Type: Article

References (28)

1. V. Scarani and N. Gisin, Phys. Rev. Lett. 87, 117901 (2001)
2. V. Scarani and N. Gisin, Phys. Rev. A 65, 012311 (2001), and references therein.
3. A. Acín, Phys. Rev. Lett. 88, 027901 (2002)
4. A. Acín, V. Scarani, and M.M. Wolf, e-print quant-ph/0112102
5. A. Acín, V. Scarani, and M.M. Wolf, Phys. Rev. A 66, 042323 (2002).
6. M. Zukowski, A. Zeilinger, M. Horne, and H. Weinfurter, Acta Phys. Pol. 93, 187 (1998).
7. M. Hillery, V. Buẑek, and A. Berthiaume, Phys. Rev. A 59, 1829 (1999).
8. H. Weinfurter and M. Zukowski, Phys. Rev. A 64, 010102
9. R.F. Werner and M.M. Wolf, ibid. 64, 032112 (2001).
10. M. Zukowski and Ĉ. Brukner, Phys. Rev. Lett. 88, 210401 (2002).
11. Ĉ. Brukner, M. Zukowski, and A. Zeilinger, Phys. Rev. Lett. 89, 197901 (2002)
12. Ĉ. Brukner, M. Zukowski, J.-W. Pan, and A. Zeilinger, e-print quant-ph/0210114.
13. Note here that the task that we deal with is to secretly share a classical bit, in the way mentioned in the text. More general tasks of secretly sharing a quantum bit has been considered (see Ref. [9]). However, these general tasks do not concern us here.
14. R. Cleve, D. Gottesman, and H.-K. Lo, Phys. Rev. Lett. 83, 648 (1999)
15. D. Gottesman, Phys. Rev. A 61, 042311 (2000)
16. D.P. DiVincenzo, P. Hayden, and B.M. Terhal, e-print quant-ph/0207147.
17. N. Linden, S. Popescu, and W.K. Wootters, Phys. Rev. Lett. 89, 207901 (2002)
18. N. Linden and W.K. Wootters, ibid. 89, 277906 (2002).
19. A.K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
20. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
21. C. H. Bennett and G. Brassard, in Proceedings of the International Conference on Computers, Systems and Signal Processing, Bangalore, India (IEEE, New York, 1984)
22. C.H. Bennett, G. Brassard, and N.D. Mermin, Phys. Rev. Lett. 68, 557 (1992).
23. C.A. Fuchs, N. Gisin, R.B. Griffiths, C.-S. Niu, and A. Peres, Phys. Rev. A 56, 1163 (1997).
24. I. Csiszár and J. Körner, IEEE Trans. Inf. Theory IT-24, 339 (1978).
25. S. Popescu and D. Rohrlich, Phys. Lett. A 166, 293 (1992).
26. A. Sen (De), U. Sen, M. Wieśniak, D. Kaszlikowski, and M. Zukowski, e-print quant-ph/0211023.
27. R. Horodecki, P. Horodecki, and M. Horodecki, Phys. Lett. A 200, 340 (1995).
28. Here one must note that secret sharing by the GHZ state has the added feature that if any one of the Bobs are left out, the remaining Bobs are with strictly no information. We however do not deal with this extreme case. In our protocol, if any of the Bobs are left out, the remaining Bobs cannot obtain the complete information about Alice's bit.