Geometric picture of entanglement and bell inequalities

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 66, Issue 3, 2002, Pages 323191-323199

  Bertlmann, R A ^a   Narnhofer, H ^a   Thirring, W ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; SET THEORY; TENSORS; THEOREM PROVING; VECTORS;

BELL INEQUALITIES;

QUANTUM THEORY;

EID: 0036756837     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (42)

1. E. Schrödinger, Naturwissenschaften 23, 807 (1935); 23 823 (1935); 23, 844 (1935).
2. E. Schrödinger, Naturwissenschaften 23, 807 (1935); 23 823 (1935); 23, 844 (1935).
3. E. Schrödinger, Naturwissenschaften 23, 807 (1935); 23 823 (1935); 23, 844 (1935).
4. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
5. A.K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
6. D. Deutsch and A.K. Ekert, Phys. World 11(3), 47 (1998).
7. R.J. Hughes, Contemp. Phys. 36, 149 (1995).
8. W. Tittel, G. Ribordy, and N. Gisin, Phys. World 11(3), 41 (1998); W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, Phys. Rev. Lett. 81, 3563 (1998).
9. W. Tittel, G. Ribordy, and N. Gisin, Phys. World 11(3), 41 (1998); W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, Phys. Rev. Lett. 81, 3563 (1998).
10. C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
11. J.-W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, Nature (London) 390, 575 (1997).
12. A. Zeilinger, Phys. World 11(3), 35 (1998).
13. The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computations, edited by D. Bouwmeester, A. Ekert, and A. Zeilinger (Springer-Verlag, Berlin, 2000).
14. J.S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, England, 1987).
15. M. Horodecki, P. Horodecki, and R. Horodecki, in Quantum Information, edited by G. Alber et al., Springer Tracts in Modern Physics Vol. 173 (Springer-Verlag, Berlin, 2001), p. 151.
16. B.M. Terhal, e-print quant-ph/0101032.
17. C.H. Bennett, D.P. Di Vincenzo, J.A. Smolin, and W.K. Wootters, Phys. Rev. A 54, 3824 (1996).
18. A.S. Holevo, Probl. Inf. Transm. 5, 247 (1979).
19. V. Vedral, M.B. Plenio, M.A. Rippin, and P.L. Knight, Phys. Rev. Lett. 78, 2275 (1997).
20. O. Rudolph, e-print math-ph/0005011.
21. H. Narnhofer, University of Vienna Report No. UWThPh-2001-25, Rep. Math. Phys. (to be published).
22. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 84, 2014 (2000).
23. C. Witte and M. Trucks, Phys. Lett. A 257, 14 (1999).
24. M. Ozawa, Phys. Lett. A 268, 158 (2000).
25. A. Uhlmann, Wiss. Z.-Karl-Marx-Univ. Leipzig, Math.-Naturwiss. Reihe 21, 421 (1972); 22, 139 (1973).
26. A. Uhlmann, Wiss. Z.-Karl-Marx-Univ. Leipzig, Math.-Naturwiss. Reihe 21, 421 (1972); 22, 139 (1973).
27. E.M. Henley and W. Thirring, Elementary Quantum Field Theory (McGraw Hill, New York, 1962).
28. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A 223, 1 (1996).
29. M.B. Terhal, Phys. Lett. A 271, 319 (2000).
30. J.F. Clauser, M.A. Home, A. Shimony, and R.A. Holt, Phys. Rev. Lett. 23, 880 (1969).
31. P. Hayden, B.M. Terhal, and A. Uhlmann, e-print quant-ph/0011095.
32. S. Hill and W.K. Wootters, Phys. Rev. Lett. 78, 5022 (1997).
33. F. Benatti, H. Narnhofer, and A. Uhlmann, Rev. Mod. Phys. 38, 123 (1996).
34. R.F. Werner, Phys. Rev. A 40, 4277 (1989).
35. R.F. Werner and M.M. Wolf, e-print quant-ph/0107093.
36. N. Gisin, Phys. Lett. A 154, 201 (1991).
37. J.S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1964).
38. F. Verstraete, J. Dehaene, and B. De Moor, e-print quant-ph/0107155.
39. R. Horodecki and M. Horodecki, Phys. Rev. A 54, 1838 (1996).
40. K.G.H. Vollbrecht and R.F. Werner, e-print quant-ph/0010095.
41. R.A. Bertlmann, W. Grimus, and B.C. Hiesmayr, Phys. Rev. D 60, 114032 (1999).
42. R.A. Bertlmann and W. Grimus, Phys. Rev. D 64, 056004 (2001).