Two-setting Bell inequalities for graph states

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 73, Issue 2, 2006, Pages

  Tóth, Géza ^a,b   Gühne, Otfried ^c   Briegel, Hans J ^c,d  

^a MAX PLANCK INSTITUT FÜR QUANTENOPTIK   (Germany)

^b INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

^c ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

^d UNIVERSITY OF INNSBRUCK   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

CORRELATION METHODS; MATHEMATICAL MODELS;

BELL INEQUALITIES; CONVEX POLYTOPE; HIDDEN VARIABLE MODELS;

GRAPH THEORY;

EID: 33144475553     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.73.022303     Document Type: Article

References (47)

1. J. S. Bell, Physics (Long Island City, N.Y.) PYCSAP 0554-128X 10.1103/PhysRev.47.777 1, 195 (1964);
2. for a review see R. Werner and M. Wolf, Quantum Inf. Comput. QICUAW 1533-7146 10.1111/j.1530-2415.2001..x 1, 1 (2001);
3. for results on multipartite Bell inequalities see Refs.; and G. Svetlichny, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.35.3066 35, 3066 (1987);
4. A. V. Belinskii and D. N. Klyshko, Usp. Fiz. Nauk UFNAAG 0042-1294 163 (8), 1 (1993);
5. N. Gisin and H. Bechmann-Pasquinucci, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(98)00516-7 246, 1 (1998);
6. A. Peres, Found. Phys. FNDPA4 0015-9018 10.1023/A:1018816310000 29, 589 (1999);
7. D. Collins, N. Gisin, S. Popescu, D. Roberts, and V. Scarani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.170405 88, 170405 (2002);
8. W. Laskowski, T. Paterek, M. Zukowski, and C. Brukner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.200401 93, 200401 (2004).
9. M. Froissart, Nuovo Cimento Soc. Ital. Fis., B NIFBAP 0369-4100 64, 241 (1981).
10. N. D. Mermin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.65. 1838 65, 1838 (1990).
11. M. Ardehali, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.46.5375 46, 5375 (1992).
12. S. Popescu and D. Rohrlich, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(92)90711-T 166, 293 (1992).
13. I. Pitowsky and K. Svozil, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.014102 64, 014102 (2001).
14. M. Żukowski and C. Brukner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.210401 88, 210401 (2002).
15. R. F. Werner and M. M. Wolf, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.032112 64, 032112 (2001).
16. R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.4277 40, 4277 (1989).
17. A. Acín (private communication);
18. A. Acín, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88. 027901 88, 027901 (2002);
19. A. Acín, V. Scarani, and M. M. Wolf, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.042323 66, 042323 (2001).
20. C. Brukner, M. Żukowski, J.-W. Pan, and A. Zeilinger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.127901 92, 127901 (2004).
21. W. Dür, H. Aschauer, and H. J. Briegel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.107903 91, 107903 (2003).
22. M. Hein, J. Eisert, and H. J. Briegel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.062311 69, 062311 (2004).
23. M. Van den Nest, J. Dehaene, and B. De Moor, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.014307 72, 014307 (2005);
24. M. Van den Nest, J. Dehaene, and B. De Moor, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.022316 69, 022316 (2004);
25. M. Van den Nest, J. Dehaene, and B. De Moor, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.034302 70, 034302 (2004);
26. K. M. R. Audenaert and M. B. Plenio, New J. Phys. NJOPFM 1367-2630 7, 170 (2005);
27. A. Hamma, R. Ionicioiu, and P. Zanardi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.012324 72, 012324 (2005);
28. D. E. Browne and T. Rudolph, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.010501 95, 010501 (2005).
29. For experimental implementations see Refs. and O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hnsch, and I. Bloch, Nature (London) NATUAS 0028-0836 10.1038/nature02008 425, 937 (2003);
30. A.-N. Zhang, C.-Y. Lu, X.-Q. Zhou, Y.-A. Chen, Z. Zhao, T. Yang and J.-W. Pan, e-print quant-ph/0501036.
31. D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.16243 58, 1131 (1990).
32. H. J. Briegel and R. Raussendorf, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.910 86, 910 (2001).
33. R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.5188 86, 5188 (2001);
34. M. A. Nielsen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93. 040503 93, 040503 (2004).
35. P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, Nature (London) NATUAS 0028-0836 10.1038/nature03347 434, 169 (2005);
36. N. Kiesel, C. Schmid, U. Weber, G. Tóth, O. Gühne, R. Ursin, and H. Weinfurter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95. 210502 95, 210502 (2005).
37. D. Schlingemann and R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.012308 65, 012308 (2002);
38. M. Grassl, A. Klappenecker and M. Rötteler, in Proceedings of the 2002 IEEE International Symposium on Information Theory, Lausanne, Switzerland (IEEE, New York, 2002);
39. K. Chen, H.-K. Lo, e-print quant-ph/0404133.
40. D. Gottesman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.1862 54, 1862 (1996).
41. V. Scarani, A. Acín, E. Schenck, and M. Aspelmeyer, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.042325 71, 042325 (2005).
42. D. P. DiVincenzo and A. Peres, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.55.4089 55, 4089 (1997).
43. O. Gühne, G. Tóth, P. Hyllus, and H. J. Briegel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.120405 95, 120405 (2005).
44. J. I. Cirac (private communication).
45. In this case the stabilizing terms in B (i) and B (j) commute locally. See G. Tóth and O. Gühne, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.022340 72, 022340 (2005).
46. Stefano Pironio, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1928727 46, 062112 (2005).
47. P. Walther, M. Aspelmeyer, K. J. Resch, and A. Zeilinger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.020403 95, 020403 (2005).