Maximal violation of a bipartite three-setting, two-outcome Bell inequality using infinite-dimensional quantum systems

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 82, Issue 2, 2010, Pages

  Pál, Károly F ^a   Vértesi, Tamás ^a  

^a INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

BELL INEQUALITIES; CLAUSER-HORNE-SHIMONY-HOLT INEQUALITY; FINITE-DIMENSIONAL QUANTUM SYSTEMS; HILBERT; ITERATIVE ALGORITHM; QUANTUM SYSTEM; QUANTUM VALUES; SPACE DIMENSIONS;

ALGORITHMS; HILBERT SPACES; MATHEMATICAL OPERATORS; QUANTUM ELECTRONICS; QUANTUM OPTICS;

BELLS;

EID: 77956326777     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.82.022116     Document Type: Article

References (47)

1. J. S. Bell, Physics 1, 195 (1964).
2. A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.230501 98, 230501 (2007).
3. S. Pironio, Nature (London) NATUAS 0028-0836 10.1038/nature09008 464, 1021 (2010).
4. C. E. Bardyn, T. C. H. Liew, S. Massar, M. McKague, and V. Scarani, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.062327 80, 062327 (2009).
5. J. Clauser, M. Horne, A. Shimony, and R. Holt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.23.880 23, 880 (1969).
6. B. S. Tsirelson, Lett. Math. Phys. LMPHDY 0377-9017 10.1007/BF00417500 4, 93 (1980).
7. B. S. Tsirelson, Hadron. J. Suppl. 8, 329 (1993).
8. Ll. Masanes, e-print arXiv: quant-ph/0309137.
9. S. Wehner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.022110 73, 022110 (2006).
10. M. Navascués, S. Pironio, and A. Acín, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.010401 98, 010401 (2007).
11. M. Navascués, S. Pironio, and A. Acín, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/10/7/073013 10, 073013 (2008).
12. R. Cleve, P. Hoyer, B. Toner, and J. Watrous, e-print arXiv: quant-ph/0404076v2.
13. K. F. Pál and T. Vértesi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.022120 79, 022120 (2009).
14. S. Zohren and R. D. Gill, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.120406 100, 120406 (2008);
15. S. Zohren, P. Reska, R. D. Gill, and W. Westra, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/90/10002 90, 10002 (2010).
16. N. Linden, S. Popescu, A. J. Short, and A. Winter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.180502 99, 180502 (2007);
17. K. F. Pál and T. Vértesi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.042114 80, 042114 (2009);
18. M. L. Almeida, J. D. Bancal, N. Brunner, A. Acín, N. Gisin, and S. Pironio, Phys. Rev. Lett. 10.1103/PhysRevLett.104.230404 104, 230404 (2010).
19. A. C. Doherty, Y. C. Liang, B. Toner, and S. Wehner, e-print arXiv: 0803.4373.
20. K. F. Pál and T. Vértesi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.042105 77, 042105 (2008).
21. N. Brunner and N. Gisin, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2008.01.052 372, 3162 (2008).
22. D. Avis, H. Imai, T. Ito, and Y. Sasaki, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/50/007 38, 10971 (2005).
23. [www.atomki.hu/atomki/TheorPhys/Bell-violation/].
24. M. Froissart, Nuovo Cimento B NCIBAW 0369-3554 10.1007/BF02903286 64, 241 (1981).
25. C. Sliwa, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(03)01115-0 317, 165 (2003).
26. D. Collins and N. Gisin, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/ 37/5/021 37, 1775 (2004).
27. A. A. Méthot and V. Scarani, Quantum Inf. Comput. 7, 157 (2007).
28. J. D. Bancal, N. Gisin, and S. Pironio, J. Phys. A 1751-8113 10.1088/1751-8113/43/38/385303 43, 385303 (2010).
29. R. F. Werner and M. M. Wolf, Quantum Inf. Comput. 1, 1 (2001).
30. T. Ito, H. Imai, and D. Avis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.042109 73, 042109 (2006).
31. Y. C. Liang and A. C. Doherty, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.052116 73, 052116 (2006);
32. Y. C. Liang and A. C. Doherty, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.042103 75, 042103 (2007).
33. Y. C. Liang, C. W. Lim, and D. L. Deng, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.052116 80, 052116 (2009).
34. N. Brunner, S. Pironio, A. Acín, N. Gisin, A. A. Méthot, and V. Scarani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.210503 100, 210503 (2008).
35. J. Briët, H. Buhrman, and B. Toner, e-print arXiv: 0901.2009;
36. T. Vértesi and K. F. Pál, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.042106 79, 042106 (2009).
37. M. Junge, C. Palazuelos, D. Pérez-García, I. Villanueva, and M. M. Wolf, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.170405 104, 170405 (2010);
38. e-print arXiv: 0910.4228.
39. T. Vértesi, S. Pironio, and N. Brunner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.060401 104, 060401 (2010).
40. D. Pérez-García, M. M. Wolf, C. Palazuelos, I. Villanueva, and M. Junge, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/s00220-008-0418-4 279, 455 (2008).
41. S. Wehner, M. Christandl, and A. C. Doherty, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.062112 78, 062112 (2008);
42. R. G. López, Master's thesis, ICFO-Institut de Ciencies Fotoniques (2009).
43. B. Borchers, Optim. Methods Software OMSOE2 1055-6788 10.1080/10556789908805764 11, 597 (1999);
44. B. Borchers, Optim. Methods Software OMSOE2 1055-6788 10.1080/10556789908805765 11, 613 (1999);
45. B. Borchers and J. G. Young, Comput. Optim. Appl. CPPPEF 0926-6003 10.1007/s10589-007-9030-3 37, 355 (2007);
46. [https://projects.coin-or.org/Csdp/].
47. J. Povh, F. Rendl, and A. Wiegele, Computing CPPPEF 0010-485X 10.1007/s00607-006-0182-2 78, 277 (2006).