Bell inequalities and entanglement

Quantum Information and Computation

Volumn 1, Issue 3, 2001, Pages 1-25

  Werner, Reinhard F ^a   Wolf, Michael M ^a  

^a TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

Author keywords

Bell inequalities; Entanglement; Local hidden variable theories

Indexed keywords

INFORMATION THEORY; QUANTUM ENTANGLEMENT;

BELL INEQUALITIES; BELL-INEQUALITY VIOLATIONS; CONVEX GEOMETRY; ENTANGLEMENT; ENTANGLEMENT PROPERTIES; LOCAL HIDDEN VARIABLE THEORY; MULTIPARTITE SYSTEMS; QUANTUM INFORMATION THEORY;

BELLS;

EID: 0011408493     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (86)

1. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
2. E. Schrödinger, Naturwissenschaften 23, 807-812; 823-828; 844-849 (1935).
3. N. Bohr, Nature 136, 65 (1935); Phys. Rev. 48, 696 (1935).
4. N. Bohr, Nature 136, 65 (1935); Phys. Rev. 48, 696 (1935).
5. D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs, New York, 1951).
6. J.S. Bell, Physics 1, 195 (1964).
7. A. Aspect, P. Grangier, and G. Roger, Phys. Rev. Lett. 47, 460 (1981).
8. M. A. Rowe et al., Nature 409, 791 (2001).
9. R.F. Werner, Phys. Rev. A 40, 4277 (1989).
10. S. Popescu, Phys. Rev. Lett. 74, 2619 (1995).
11. C.H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. Smolin, and W.K. Wootters, Phys. Rev. Lett. 76, 722 (1996).
12. N. Gisin, Phys. Lett. A 210, 151 (1996).
13. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 80, 5239 (1998).
14. R.F. Werner and M.M. Wolf, Phys. Rev. A 61, 062102 (2000).
15. R.F. Werner and M.M. Wolf, quant-ph/0102024 (2001).
16. W. Dür, quant-ph/0107050 (2001).
17. A. Cabello, Phys. Rev. Lett. 86, 1911 (2001).
18. J.F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978).
19. D. Home and F. Selleri, Riv. Nuovo Cimento 14, 1 (1991).
20. A. Garg and N.D. Mermin, Found. Phys. 14, 1 (1984).
21. N.D. Mermin, Rev. Mod. Phys. 65, 803 (1993).
22. J.v. Neumann, Mathematische Grundlagen der Quantenmechanik, (Springer, Berlin, 1932).
23. D. Bohm, Phys. Rev. 85, 166 (1952); 85, 180 (1952).
24. D. Bohm, Phys. Rev. 85, 166 (1952); 85, 180 (1952).
25. E. Nelson, Dynamical Theories of Brownian Motion, (Princeton University Press 1967).
26. R.F. Werner, Phys. Rev D 34, 463 (1986).
27. A. Fine, Phys. Rev. Lett. 48, 291 (1982); A. Fine, J. Math. Phys. 23, 1306 (1982).
28. A. Fine, Phys. Rev. Lett. 48, 291 (1982); A. Fine, J. Math. Phys. 23, 1306 (1982).
29. J. F. Clauser, M. A. Home, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).
30. R.F. Werner in Quantum Information - an introduction to basic theoretical concepts and experiments (Springer tracts in modern physics, Berlin, 2001).
31. I. Pitowsky, Quantum Probability - Quantum Logic (Springer, Berlin, 1989).
32. I. Pitowsky, Mathematical Programming 50, 395 (1991).
33. M. Zukowski and C. Brukner, quant-ph/0102039 (2001).
34. I. Pitowsky and K. Svozil, quant-ph/0011060 (2000).
35. A list of the coefficients belonging to the 53856 inequalities for the case (n, m, v) = (3,2,2) can be found on http://tph.tuwien.ac.at/svozil/publ/ghzbig.html.
36. N. Gisin, Phys. Lett. A 260, 1 (1999).
37. N.D. Mermin, Phys. Rev. Lett. 65, 3373 (1990).
38. D. Kaszlikowski, P. Gnacinski, M. Zukowski, W. Miklaszewski, and A. Zeilinger, Phys. Rev. Lett. 85, 4418 (2000).
39. A. Garg and N.D. Mermin, Phys. Rev. Lett. 49, 1220 (1982).
40. N. D. Mermin, Phys. Rev. Lett. 65, 1838 (1990).
41. M. Ardehali, Phys. Rev. A 46, 5375 (1992).
42. S. M. Roy and V. Singh, Phys. Rev. Lett. 67, 2761 (1991).
43. A. V. Belinskii and D. N. Klyshko, Sov. Phys. Usp. 36, 653 (1993).
44. N. Gisin and H. Bechmann-Pasquinucci, Phys. Lett. A 246, 1 (1998).
45. A. Peres, Found. Phys. 29, 589 (1999).
46. A. Peres, Phys. Rev. Lett. 77, 1413 (1996).
47. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, Phys. Rev. Lett. 76, 722 (1996).
48. B. S. Cirel'son, Lett. Math. Phys. 4, 93 (1980).
49. L. J. Landau, Phys. Lett. A 120, 54 (1987).
50. S.J. Summers and R.F. Werner, Commun. Math. Phys. 110, 247 (1987).
51. S.J. Summers and R.F. Werner, Ann. Inst. Henri Poincaré 49, 215 (1988).
52. V. Scarani and N. Gisin, quant-ph/0103068 (2001).
53. R. Horodecki, P. Horodecki, and M. Horodecki, Phys. Lett. A 200, 340 (1995).
54. N. Gisin, Phys. Lett. A 154, 201 (1991).
55. N. Gisin and A. Peres, Phys. Lett. A 162, 15 (1992).
56. S. Popescu and D. Rohrlich, Phys. Lett. A 166, 293 (1992).
57. K. Banaszek and K. Wódkiewicz, Phys. Rev. A 58, 4345 (1998).
58. K. Banaszek and K. Wódkiewicz, Phys. Rev. Lett. 82, 2009 (1999).
59. H. Jeong, J. Lee, M.S. Kim, Phys. Rev. A 61, 052101 (2000).
60. Z.-B. Chen, J.-W. Pan, G. Hou, and Y.-D. Zhang, quant-ph/0103051 (2001).
61. R. Haag and D. Kastler, J. Math. Phys. 5, 848 (1964).
62. R. Haag, Local Quantum Physics, Springer (1992).
63. S.J. Summers and R.F. Werner, Phys. Lett. A 110, 257 (1985).
64. R. Verch and R.F. Werner, in preparation.
65. S.L. Braunstein and C.M. Caves, Ann. Phys. 202, 22 (1990).
66. B.S. Cirel'son, Lett. Math. Phys., 4, 93 (1980).
67. B.S. Tsirel'son, J. Sov. Math., 36, 557 (1987).
68. D.M. Greenberger, M. Home, and A. Zeilinger in Bell's Theorem, Quantum Theory, and Conceptions of the Universe, M. Kafatos, ed., Kluwer, Dordrecht (1989).
69. M. Zukowski, Phys. Lett. A 177, 290 (1993).
70. D.P. DiVincenzo, P.W. Shor, J.A. Smolin, B.M. Terhal, and A.V. Thapliyal, Phys. Rev. A 61, 062312 (2000); W. Dür, J.I. Cirac, M. Lewenstein, D. Bruss, Phys. Rev. A 61, 062313 (2000); T. Eggeling, K.G.H. Vollbrecht, R.F. Werner, and M.M. Wolf, quant-ph/0104095 (2001).
71. D.P. DiVincenzo, P.W. Shor, J.A. Smolin, B.M. Terhal, and A.V. Thapliyal, Phys. Rev. A 61, 062312 (2000); W. Dür, J.I. Cirac, M. Lewenstein, D. Bruss, Phys. Rev. A 61, 062313 (2000); T. Eggeling, K.G.H. Vollbrecht, R.F. Werner, and M.M. Wolf, quant-ph/0104095 (2001).
72. D.P. DiVincenzo, P.W. Shor, J.A. Smolin, B.M. Terhal, and A.V. Thapliyal, Phys. Rev. A 61, 062312 (2000); W. Dür, J.I. Cirac, M. Lewenstein, D. Bruss, Phys. Rev. A 61, 062313 (2000); T. Eggeling, K.G.H. Vollbrecht, R.F. Werner, and M.M. Wolf, quant-ph/0104095 (2001).
73. R. Horodecki, M. Horodecki, and P. Horodecki, quant-ph/9606027 (1996).
74. V. Scarani and N. Gisin, quant-ph/0101110 (2001).
75. V. Scarani and N. Gisin, quant-ph/0104016 (2001).
76. B. Huttner and N. Gisin, Phys. Lett. A 228, 13 (1997).
77. C. Fuchs, N. Gisin, R.B. Griffiths, C.-S. Niu, and A. Peres, Phys. Rev. A 56, 1163 (1997).
78. P.M. Gruber and J.M. Wills (editors), Handbook of convex geometry, North-Holland (1993).
79. H.H. Schaefer, Topological Vector Spaces (Springer, Berlin, 1980).
80. R. Webster, Convexity (Oxford University Press, 1994).
81. P. McMullen, J. Combin. Theory Ser. B 10, 187 (1971).
82. I. Bárány and A. Pór, 0-1 polytopes with many facets, manuscript, Rényi Institute of Mathematics, Hungarian Academy of Sciences; http://www.renyi.hu/barany/ (2000).
83. C.K. Yap, Fundamental problems in algorithmic algebra (Oxford University Press, 2000); see also http://www.ifor.math.ethz.ch/fukuda/polyfaq/ polyfaq.html for a brief review.
84. B. Chazelle, Discrete Compute. Geom. 10, 377 (1993).
85. D. Avis and K. Fukuda, Discrete Compute. Geom. 8, 295 (1992).
86. F. Barahona, J. Phys. A 15, 3241 (1982).