Quantum nonlocality without entanglement

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 59, Issue 2, 1999, Pages 1070-1091

  Bennett, Charles H ^a   DiVincenzo, David P ^a   Fuchs, Christopher A ^b   Mor, Tal ^c   Rains, Eric ^d   Shor, Peter W ^d   Smolin, John A ^a   Wootters, William K ^e  

^a IBM T J WATSON RESEARCH CENTER   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c Succursale Centre Ville   (Canada)

^d AT AND T LABS RESEARCH   (United States)

^e WILLIAMS COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000795422     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.59.1070     Document Type: Article

References (55)

1. A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
2. C. H. Bennett, C. A. Fuchs, and J. A. Smolin, in Quantum Communication, Computing, and Measurement, edited by O. Hirota, A. S. Holevo, and C. M. Caves (Plenum, New York, 1997), p. 79;
3. C. H. BennettC. A. FuchsJ. A. Smoline-print quant-ph/9611006.
4. H. Buhrman, R. Cleve, and A. Wigderson, in Proceedings of the 30th Annual ACM Symposium on the Theory of Computing, Dallas, 1998 (ACM, Los Alamitos, 1998), p. 63;
5. H. BuhrmanR. CleveA. Wigdersone-print quant-ph/9802040.
6. C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
7. P. W. Shor, SIAM J. Comput. 26, 1484 (1997), and references therein.
8. L. Grover, Phys. Rev. Lett. 79, 325 (1997).
9. W. K. Wootters and W. Zurek, Nature (London) 299, 802 (1982).
10. S. Popescu and L. Vaidman, Phys. Rev. A 49, 4331 (1994).
11. A. Peres and W. K. Wootters, Phys. Rev. Lett. 66, 1119 (1991).
12. A. S. Kholevo, Probl. Inf. Transm. 15, 247 (1979).
13. A. S. Holevo, IEEE Trans. Inf. Theory 44, 269 (1998)
14. A. S. Holevoe-print quant-ph/9611023.
15. B. Schumacher and M. D. Westmoreland, Phys. Rev. A 56, 131 (1997).
16. P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, and W. K. Wootters, Phys. Rev. A 54, 1869 (1996).
17. S. Massar and S. Popescu, Phys. Rev. Lett. 74, 1259 (1995).
18. L. Goldenberg and L. Vaidman, Phys. Rev. Lett. 75, 1239 (1995).
19. A. Peres, Phys. Rev. Lett. 77, 3264 (1996)
20. Phys. Rev. Lett.L. Goldenberg and L. Vaidman, 77, 3265 (1996).
21. T. Mor, Phys. Rev. Lett. 80, 3137 (1998)
22. T. Morquant-ph/9802036.
23. C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, 1984 (IEEE, New York, 1984), p. 175.
24. E. Rains, e-print quant-ph/9707002.
25. V. Vedral and M. B. Plenio, Phys. Rev. A 57, 1619 (1998)
26. V. VedralM. B. Plenioe-print quant-ph/9707035.
27. M. Horodecki, P. Horodecki, and R. Horodecki, e-print quant-ph/9801069.
28. H. Barnum, M. A. Nielsen, and B. Schumacher, Phys. Rev. A 57, 4153 (1998).
29. B. Schumacher, Phys. Rev. A 54, 2614 (1996)
30. B. Schumachere-print quant-ph/9604023.
31. M. A. Nielsen, C. M. Caves, B. Schumacher, and H. Barnum, Proc. R. Soc. London, Ser. A 454, 277 (1998)
32. M. A. NielsenC. M. CavesB. SchumacherH. Barnume-print quant-ph/9706064.
33. Weak measurements were introduced by Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988)
34. see also Y. Aharonov and L. Vaidman, Phys. Rev. A 41, 11 (1990), Sec. IV. The quantum gates for our weak measurements (used in our proof in Appendix A) were introduced by T. Mor, Ph.D. thesis, The Technion, 1997, Sec. 4.4 (unpublished).
35. N. Abramson, Information Theory and Coding (McGraw-Hill, New York, 1963), Chap. 5.
36. M. Ohya and D. Petz, Quantum Entropy and Its Use (Springer-Verlag, Berlin, 1993).
37. To distinguish two equiprobable pure states with overlap (Formula presented) the optimal measurement is a von Neumann measurement in the subspace spanned by the two states, in a basis symmetrically disposed around these two states. The resulting error probability is (Formula presented) so that the last two terms on the right-hand side of Eq. (34) become (Formula presented) See L. B. Levitin, in Quantum Communications and Measurement, edited by V. P. Belavkin, O. Hirota, and R. L. Hudson (Plenum, New York, 1995)
38. C. A. Fuchs and C. M. Caves, Phys. Rev. Lett. 73, 3047 (1994).
39. B. Schumacher, Phys. Rev. A 51, 2738 (1995).
40. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 54, 3824 (1996)
41. C. H. BennettD. P. DiVincenzoJ. A. SmolinW. K. Wootterse-print quant-ph/9604024.
42. R. Landauer, IBM J. Res. Dev. 5, 183 (1961).
43. It is easy to show by a process of elimination that there does not exist any product vector that is orthogonal to the four states of Eq. (58). From this we find that the density operator (Formula presented) has many fascinating entanglement properties. Among other things, it exhibits the “bound” entanglement of Ref. 21. This will be explored in a forthcoming work (D. P. DiVincenzo, T. Mor, P. W. Shor, J. A. Smolin, and B. M. Terhal, e-print quant-ph/9808030).
44. J. C. Lagarias and P. W. Shor, Bull. Am. Math. Soc. 27, 279 (1992)(see http://www.research.att.com/∼shor/papers/index.html)
45. Discrete Comput. Geom. 11, 359 (1994).
46. S. Popescu (private communication).
47. P. Høyer (private communication).
48. C. H. Bennett, G. Brassard, and N. D. Mermin, Phys. Rev. Lett. 68, 557 (1992).
49. However, see D. Aharonov, A. Kitaev, and N. Nisan, in Proceedings of the 13th Annual Symposium on the Theory of Computation, Dallas, 1998 (ACM, Los Alamitos, 1998), p. 20;
50. S. Richter and R. F. Werner, J. Stat. Phys. 82, 963 (1996).
51. C. A. Fuchs and A. Peres, Phys. Rev. A 53, 2038 (1996).
52. C. M. Caves, K. S. Thorne, R. W. P. Drever, V. D. Sandberg, and M. Zimmermann, Rev. Mod. Phys. 52, 341 (1980).
53. E. Kranakis, Primality and Cryptography (Wiley, New York, 1986), p. 94;
54. A. Rényi, Foundations of Probability (Holden-Day, San Francisco, 1970), p. 200.
55. M. N. Wegman and J. L. Carter, J. Comput. and Syst. Sci. 22, 265 (1981).