Functional Bell inequalities can serve as a stronger entanglement witness than conventional Bell inequalities

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 66, Issue 6, 2002, Pages 4-

 

^a De), Aditi   (Poland)

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EID: 85037255550     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.66.062318     Document Type: Article

References (35)

1. J.S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1964).
2. J.F. Clauser, M.A. Horne, A. Shimony, and R.A. Holt, Phys. Rev. Lett. 23, 880 (1969)
3. J.F. Clauser and M.A. Horne, Phys. Rev. D 10, 526 (1974).
4. N.D. Mermin, Phys. Rev. Lett. 65, 1838 (1990)
5. A.V. Belinskii and D.N. Klyshko, Phys. Usp. 36, 653 (1993).
6. H. Weinfurter and M. Żukowski, Phys. Rev. A 64, 010102 (2001)
7. Phys. Rev. AR.F. Werner and M.M. Wolf, 64, 032112 (2001)
8. M. Żukowski and Č. Brukner, Phys. Rev. Lett. 88, 210401 (2002).
9. A. Garuccio and F. Selleri, Found. Phys. 10, 209 (1980);S. L. Braunstein and C. M. Caves, in Proceedings of the Third International Symposium on Foundations of Quantum Mechanics, edited by S. Kobayashi et al., (Physical Soceity of Japan, Tokyo, 1989)
10. N. Gisin, Phys. Lett. A 260, 1 (1999).
11. M. Żukowski, Phys. Lett. A 177, 290 (1993).
12. D. Kaszlikowski and M. Żukowski, Phys. Rev. A 61, 022114 (2000).
13. S. Aerts, P. Kwiat, J.-Å. Larsson, and M. Żukowski, Phys. Rev. Lett. 83, 2872 (1999).
14. N. Gisin, Phys. Lett. A 154, 201 (1991)
15. Phys. Lett. AN. Gisin and A. Peres, 162, 15 (1992).
16. V. Scarani and N. Gisin, J. Phys. A 34, 6043 (2001).
17. M. Żukowski, Č. Brukner, W. Laskowski, and M. Wieśniak, Phys. Rev. Lett. 88, 210402 (2002).
18. D. M. Greenberger, M. A. Horne, and A. Zeilinger, in Bell’s Theorem, Quantum Theory, and Conceptions of the Universe, edited by M. Kafatos (Kluwer Academic, Dordrecht, The Netherlands, 1989).
19. C.H. Bennett and S.J. Wiesner, Phys. Rev. Lett. 69, 2881 (1992).
20. C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
21. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 80, 5239 (1998)
22. P. Horodecki, Phys. Lett. A 232, 233 (1997).
23. The partial transpose of a bipartite state (Formula presented) where i and j are the indices for party A and (Formula presented) and (Formula presented) are the indices for party B, with respect to part A is (Formula presented) 17. A state (Formula presented) is said to have positive partial transpose if (Formula presented) is a positive operator. (Formula presented) has nonpositive partial transpose otherwise.
24. A. Peres, Phys. Rev. Lett. 77, 1413 (1996).
25. A. Peres, Found. Phys. 29, 589 (1999).
26. R.F. Werner and M.M. Wolf, Phys. Rev. A 61, 062102 (2000).
27. D. Kaszlikowski, M. Żukowski, and P. Gnaciński, Phys. Rev. A 65, 032107 (2002).
28. W. Dür, Phys. Rev. Lett. 87, 230402 (2001).
29. Of course, one can show that the violation of the so-called Mermin-Klyshko inequalities considered in 21 occurs for all values of (Formula presented) for (Formula presented)
30. D. Kaszlikowski, J.L. Chen, C.H. Oh, and L.C. Kwek, e-print quant-ph/020631.
31. S. Popescu and D. Rohrlich, Phys. Lett. A 166, 293 (1992).
32. D. Kaszlikowski, D. Gosal, L. C. Kwek, M. Żukowski, and C. H. Oh (unpublished).
33. A. Acín, Phys. Rev. Lett. 88, 027901 (2002).
34. A. Acín and V. Scarani, e-print quant-ph/0112102;
35. A. Acín, V. Scarani, and M.M. Wolf, Phys. Rev. A 66, 042323 (2002).