Bell Inequalities: Many Questions, a Few Answers

Part of the The Western Ontario Series in Philosophy of Science book series (WONS, volume 73)

What can be more fascinating than experimental metaphysics, to quote one of Abner Shimony's enlightening expressions? Bell inequalities are at the heart of the study of nonlocality. I present a list of open questions, organised in three categories: fundamental; linked to experiments; and exploring nonlocality as a resource. New families of inequalities for binary outcomes are presented.

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References

  1. 1.
    A.K. Ekert, Phys. Rev. Lett. 67, 661–663 (1991).MATHCrossRefMathSciNetADSGoogle Scholar
  2. 2.
    I. Pitowski, Quantum Probability — Quantum Logic, (Lecture Notes in Physics, Vol. 321). Berlin, Springer-Verlag 1989.Google Scholar
  3. 3.
    J.F. Clauser, M.A. Horne, A. Shimony and R.A. Holt, Phys. Rev. Lett. 23, 880 (1969).CrossRefADSGoogle Scholar
  4. 4.
  5. 5.
    D. Collins and N. Gisin, J. Phys. A: Math. Gen. 37, 1775 (2004).MATHCrossRefMathSciNetADSGoogle Scholar
  6. 6.
    R.F. Werner, Phys. Rev. A 40, 4277 (1989).CrossRefADSGoogle Scholar
  7. 7.
    A. Acin, N. Gisin and B. Toner, Phys. Rev. A 73, 062105 (2006).CrossRefMathSciNetADSGoogle Scholar
  8. 8.
    D. Kaszlikowski et al., Phys. Rev. Lett. 85, 4418 (2000).CrossRefADSGoogle Scholar
  9. 9.
    D. Collins, N. Gisin, N. Linden, S. Popescu and S. Massar, Phys. Rev. Lett. 88, 040404 (2002).CrossRefMathSciNetADSGoogle Scholar
  10. 10.
    M.L. Almeida et al, quant-ph/0703018.Google Scholar
  11. 11.
    S. Popescu, Phys. Rev. Lett. 74, 2619–2622 (1995).MATHCrossRefMathSciNetADSGoogle Scholar
  12. 12.
    N. Gisin, Phys. Lett. A 210, 151–156 (1996); ibid. 224, 317–318 (1997).CrossRefMathSciNetADSMATHGoogle Scholar
  13. 13.
    J. Barrett, Phys. Rev. A bf65, 042302 (2002).CrossRefMathSciNetADSGoogle Scholar
  14. 14.
    B.M. Therhal, A. Doherty and D. Schwab, Phys. Rev. Lett. 90, 157903 (2003).CrossRefMathSciNetADSGoogle Scholar
  15. 15.
    A. Acin, T. Durt, N. Gisin and J.I. Latorre, Phys. Rev. A 65, 052325 (2002).CrossRefADSGoogle Scholar
  16. 16.
    A.A. Méthot and V. Scarani, Quant. Inf. Comput. 7, 157 (2007).MATHGoogle Scholar
  17. 17.
    H. Bechmann-Pasquinucci and N. Gisin, Phys. Rev. A 67, 062310, 2003. See also appendix B.CrossRefMathSciNetADSGoogle Scholar
  18. 18.
    N. Gisin, Phys. Lett. A 154, 201–202 (1991).CrossRefMathSciNetADSGoogle Scholar
  19. 19.
    N. Gisin and A. Peres, Phys. Lett. A 162, 15–17 (1992).CrossRefMathSciNetADSGoogle Scholar
  20. 20.
    N.D. Mermin, Phys. Rev. Lett. 65, 1838 (1990).MATHCrossRefMathSciNetADSGoogle Scholar
  21. 21.
    A.V. Belinskii and D.N. Klyshko, Phys. Usp. 36, 653 (1993).CrossRefADSGoogle Scholar
  22. 22.
    A. Acin et al., Phys. Rev. Lett. 92, 250404 (2004).CrossRefMathSciNetADSGoogle Scholar
  23. 23.
    J.-L. Chen, Phys. Rev. Lett. 93, 140407 (2004).CrossRefMathSciNetADSGoogle Scholar
  24. 24.
    S. Popescu and D. Rohrlich, Phys. Lett. A 166, 293–297 (1992).CrossRefMathSciNetADSGoogle Scholar
  25. 25.
    R. Cleve, P. Hoyer, B. Toner and J. Watrous, quant-ph/0404076.Google Scholar
  26. 26.
    L. Masanes, Phys. Rev. Lett. 97, 050503 (2006).CrossRefMathSciNetADSGoogle Scholar
  27. 27.
    W. Dür, Phys. Rev. Lett. 87, 230402 (2001).CrossRefMathSciNetADSGoogle Scholar
  28. 28.
    N. Gisin and H. Bechmann-Pasquinucci, Phys. Lett. A 246, 1–6 (1998).MATHCrossRefMathSciNetADSGoogle Scholar
  29. 29.
    A. Acin, Phys. Rev. Lett. 88, 027901 (2001).CrossRefMathSciNetADSGoogle Scholar
  30. 30.
    A. Acin, V. Scarani and M. Wolf, Phys. Rev. A 66, 04323 (2002).CrossRefMathSciNetGoogle Scholar
  31. 31.
    G. Svetlichny, Phys. Rev. D 35, 3066 (1987).CrossRefMathSciNetADSGoogle Scholar
  32. 32.
    D. Collins et al., Phys. Rev. Lett. 88, 170405 (2002).CrossRefADSGoogle Scholar
  33. 33.
    M. Seevinck and G. Svetlichny, Phys. Rev. Lett. 89, 060401 (2002).CrossRefMathSciNetADSGoogle Scholar
  34. 34.
    J.L. Cereceda, Phys. Rev. A 66, 024102 (2002).CrossRefMathSciNetADSGoogle Scholar
  35. 35.
    K. Nagata, W. Laskowski and T. Paterek, Phys. Rev. A 74, 062109 (2006).CrossRefADSGoogle Scholar
  36. 36.
    M. Horodecki, P. Horodecki and R. Horodecki, Phys. Lett. A 200, 340 (1995).MATHCrossRefMathSciNetADSGoogle Scholar
  37. 37.
    J.S Bell, Physics 1, 195–200 (1964); reprinted in: J.S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, (Cambridge University Press, Cambridge, 1987, revised edition 2004).Google Scholar
  38. 38.
    Ph. Pearle, Phys.Rev. D 2, 1418 (1970).CrossRefADSGoogle Scholar
  39. 39.
    B. Gisin and N. Gisin, Phys. Lett. A 260, 323–327 (1999).MATHCrossRefMathSciNetADSGoogle Scholar
  40. 40.
    S. Massar, S. Pironio, J. Roland and B. Gisin, Phys. Rev. A 66, 052112 (2002).CrossRefADSGoogle Scholar
  41. 41.
    H. Buhrman, P. Hoyer, S. Massar and H. Roehrig, Phys. Rev. Lett. 91, 047903 (2003).CrossRefADSGoogle Scholar
  42. 42.
    Ph. Eberhard, Phys. Rev. A 47, R747 (1993).CrossRefADSGoogle Scholar
  43. 43.
    J. Volz et al., Phys. Rev. Lett. 96, 030404 (2006).CrossRefADSGoogle Scholar
  44. 44.
    A. Cabello and J.-A. Larsson, quant-ph/0701191, Phys. Rev. Lett. 98, 220402 (2007).CrossRefADSGoogle Scholar
  45. 45.
    N. Brunner, N. Gisin, V. Scarani and Ch. Simon, quant-ph/0702130, Phys. Rev. Lett. 98, 220403 (2007).CrossRefADSGoogle Scholar
  46. 46.
    R. Garca-Patrón, J. Fiurácek, N.J. Cerf, J. Wenger, R. Tualle-Brouri and Ph. Grangier, Phys. Rev. Lett. 93, 130409 (2004).CrossRefADSGoogle Scholar
  47. 47.
    M. Zukowski, Phys. Lett. A 177, 290 (1993). See also quant-ph/9908009.CrossRefMathSciNetADSGoogle Scholar
  48. 48.
    N. Gisin, Phys. Lett. A 260, 1–3 (1999).MATHCrossRefMathSciNetADSGoogle Scholar
  49. 49.
    J. Barrett et al., Phys. Rev. A 71, 022101 (2005).CrossRefMathSciNetADSGoogle Scholar
  50. 50.
    S. Popescu and D. Rohrlich, Found. Phys. 24, 379–385, (1994).CrossRefMathSciNetADSGoogle Scholar
  51. 51.
    N. Cerf, N. Gisin and S. Massar, Phys. Rev. Lett. 94, 220403 (2005).CrossRefADSGoogle Scholar
  52. 52.
    J. Barrett and S. Pironio, Phys. Rev. Lett. 95, 140401 (2005).CrossRefADSGoogle Scholar
  53. 53.
    F. Dupuis et al., quant-ph/0701142.Google Scholar
  54. 54.
    D. Bacon and B. Toner, Phys. Rev. Lett. 90, 157904 (2003).CrossRefMathSciNetADSGoogle Scholar
  55. 55.
    N. Brunner, N. Gisin and V. Scarani, New J. Phys. 7, 1–14 (2005).CrossRefGoogle Scholar
  56. 56.
    N. Brunner, V. Scarani and N. Gisin, J. Math. Phys. 47, 112101 (2006).CrossRefMathSciNetADSGoogle Scholar
  57. 57.
    B.S. Tsirelson, Lett. Math. Phys. 4, 83, 1980.MathSciNetGoogle Scholar
  58. 58.
    M. Navascues, S. Pironio and A. Acin, quant-ph/0607119.Google Scholar
  59. 59.
    J. Barrett, L. Hardy and A. Kent, Phys. Rev. Lett. 95, 010503 (2005).CrossRefADSGoogle Scholar
  60. 60.
    V. Scarani, N. Gisin, N. Brunner, L. Masanes, S. Pironio and A. Acin, Phys. Rev. A 74, 042339 (2006).CrossRefADSGoogle Scholar
  61. 61.
    A. Acin, N. Gisin and Lluis Masanes, Phys. Rev. Lett. 97, 120405 (2006).CrossRefADSGoogle Scholar
  62. 62.
    N. Gisin and S. Wolf, Phys. Rev. Lett. 83, 4200–4203 (1999).CrossRefADSGoogle Scholar
  63. 63.
    N. Gisin, R. Renner and S. Wolf, Algorithmica 34, 389–412 (2002).MATHCrossRefMathSciNetGoogle Scholar
  64. 64.
    C. Sliwa, Phys. Lett. A 317, 165–168 (2003).MATHCrossRefMathSciNetADSGoogle Scholar
  65. 65.
    D. Avis, H. Imai and T. Ito, J. Phys. A 39, 11283–11299 (2006).MATHCrossRefMathSciNetADSGoogle Scholar
  66. 66.
    Isaac Newton, Papers & Letters on Natural Philosophy and related documents, page 302, Edited, with a general introduction, by Bernard Cohen, assisted by Robert E. Schofield Harvard University Press, Cambridge, Massachusetts, 1958.Google Scholar
  67. 67.
    N. Gisin, Can relativity be considered complete? From Newtonian nonlocality to quantum nonlocality and beyond, quant-ph/0512168.Google Scholar
  68. 68.
    Brassard, G., Q communication complexity, quant-ph/0101005.Google Scholar

Copyright information

© Springer Science+Business Media B.V 2009

Authors and Affiliations

  1. 1.Group of Applied PhysicsUniversity of GenevaSwitzerland

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