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Quantum Bounds for Temporal Correlations

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Part of the Springer Theses book series (Springer Theses)

Abstract

The assumptions of realism and locality lead to bounds on the correlations between observable quantities—the Bell inequalities, and these bounds are violated in quantum mechanics.

Keywords

Positive Semidefinite Projective Measurement Bell Inequality Semidefinite Program Sequential Measurement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    J.F. Clauser, M.A. Horne, A. Shimony, R.A. Holt, Phys. Rev. Lett. 23, 880 (1969). doi: 10.1103/PhysRevLett.23.880 Google Scholar
  2. 2.
    B.C. Cirel’son, Lett. Math. Phys. 4, 93 (1980)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    S. Popescu, D. Rohrlich, Found. Phys. 24, 379 (1994). doi: 10.1007/BF02058098 ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    A. Cabello, Phys. Rev. Lett. 110, 060402 (2013). doi: 10.1103/PhysRevLett.110.060402 ADSCrossRefGoogle Scholar
  5. 5.
    T. Fritz, A.B. Sainz, R. Augusiak, J. Bohr Brask, R. Chaves, A. Leverrier, A. Acín, Nat. Commun. 4, 2263 (2013). doi: 10.1038/ncomms3263
  6. 6.
    G. Brassard, H. Buhrman, N. Linden, A.A. Méthot, A. Tapp, F. Unger, Phys. Rev. Lett. 96, 250401 (2006). doi: 10.1103/PhysRevLett.96.250401 ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    M. Pawłowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, M. Żukowski, Nature (London) 461, 1101 (2009). doi: 10.1038/nature08400 ADSCrossRefGoogle Scholar
  8. 8.
    D. Gross, M. Müller, R. Colbeck, C.O. Dahlsten, Phys. Rev. Lett. 104, 080402 (2010). doi: 10.1103/PhysRevLett.104.080402 ADSCrossRefGoogle Scholar
  9. 9.
    M. Navascués, Y. Guryanova, M.J. Hoban, A. Acín (2014) arXiv:1403.4621
  10. 10.
    T. Fritz, New J. Phys 12, 083055 (2010). doi: 10.1088/1367-2630/12/8/083055 ADSCrossRefGoogle Scholar
  11. 11.
    S. Kochen, E.P. Specker, J. Math. Mech. 17, 59 (1967). doi: 10.1512/iumj.1968.17.17004 MathSciNetGoogle Scholar
  12. 12.
    A.J. Leggett, A. Garg, Phys. Rev. Lett. 54, 857 (1985). doi: 10.1103/PhysRevLett.54.857 ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    A.A. Klyachko, M.A. Can, S. Binicioğlu, A.S. Shumovsky, Phys. Rev. Lett. 101, 020403 (2008). doi: 10.1103/PhysRevLett.101.020403 ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    M. Barbieri, Phys. Rev. A 80, 034102 (2009). doi: 10.1103/PhysRevA.80.034102 ADSCrossRefGoogle Scholar
  15. 15.
    J. Kofler, C. Brukner, Phys. Rev. Lett. 101, 090403 (2008). doi: 10.1103/PhysRevLett.101.090403 ADSCrossRefGoogle Scholar
  16. 16.
    T. Fritz, J. Math. Phys. 51, 052103 (2010). doi: 10.1063/1.3377969 ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    C. Budroni, T. Moroder, M. Kleinmann, O. Gühne, Phys. Rev. Lett. 111, 020403 (2013). doi: 10.1103/PhysRevLett.111.020403 ADSCrossRefGoogle Scholar
  18. 18.
    J. von Neumann, Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932)zbMATHGoogle Scholar
  19. 19.
    G. Lüders, Ann. Phys. (Leipzig) 8, 322 (1951)Google Scholar
  20. 20.
    S. Wehner, Phys. Rev. A 73, 022110 (2006). doi: 10.1103/PhysRevA.73.022110
  21. 21.
    L. Vandenberghe, S. Boyd, SIAM Rev. 38, 49 (1996). doi: 10.1137/1038003 MathSciNetCrossRefGoogle Scholar
  22. 22.
    Y.-C. Liang, R.W. Spekkens, H.M. Wiseman, Phys. Rep. 506, 1 (2011). doi: 10.1016/j.physrep.2011.05.001 ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    M. Araújo, M.T. Quintino, C. Budroni, M. Terra Cunha, A. Cabello, Phys. Rev. A 88, 022118 (2013). doi: 10.1103/PhysRevA.88.022118 ADSCrossRefGoogle Scholar
  24. 24.
    M. Navascués, S. Pironio, A. Acín, Phys. Rev. Lett. 98 (2007). doi: 10.1103/PhysRevLett.98.010401
  25. 25.
    M. Navascués, S. Pironio, A. Acín, New J. Phys. 10 (2008). doi: 10.1088/1367-2630/10/7/073013 Google Scholar
  26. 26.
    A.C. Doherty, Y.-C. Liang, B. Toner, S. Wehner, in Proceedings of IEEE Conference on Computational Complexity, College Park, MD, 2008 (IEEE, New York 2008), p.199Google Scholar
  27. 27.
    O. Gühne, C. Budroni, A. Cabello, M. Kleinmann, J.-Å. Larsson, Phys. Rev. A 89, 062107 (2014). doi: 10.1103/PhysRevA.89.062107 ADSCrossRefGoogle Scholar
  28. 28.
    K.F. Pál, T. Vértesi, Phys. Rev. A 82, 022116 (2010). doi: 10.1103/PhysRevA.82.022116 ADSCrossRefGoogle Scholar
  29. 29.
    T. Moroder, J.-D. Bancal, Y.-C. Liang, M. Hofmann, O. Gühne, Phys. Rev. Lett. 111, 030501 (2013). doi: 10.1103/PhysRevLett.111.030501 ADSCrossRefGoogle Scholar
  30. 30.
    S. Yu, C.H. Oh, Phys. Rev. Lett. 108, 030402 (2012). doi: 10.1103/PhysRevLett.108.030402 ADSCrossRefGoogle Scholar
  31. 31.
    A. Cabello (2011). arXiv:1112.5149
  32. 32.
    M. Kleinmann, C. Budroni, J.-Å. Larsson, O. Gühne, A. Cabello, Phys. Rev. Lett. 109, 250402 (2012). doi: 10.1103/PhysRevLett.109.250402 ADSCrossRefGoogle Scholar
  33. 33.
    M.L. Almeida, J.-D. Bancal, N. Brunner, A. Acín, N. Gisin, S. Pironio, Phys. Rev. Lett. 104, 230404 (2010). doi: 10.1103/PhysRevLett.104.230404 ADSCrossRefGoogle Scholar
  34. 34.
    R.M. Gray, Found. Trends Commun. Inf. Theory 2, 155 (2006)CrossRefGoogle Scholar
  35. 35.
    B.S. Tsirel’son, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 142, 174 (1985). (Russian, English translation [36])Google Scholar
  36. 36.
    B.S. Tsirel’son, J. Soviet Math. 36, 557 (1987)CrossRefGoogle Scholar
  37. 37.
    O. Bratteli and D.W. Robinson, Operator Algebras and Quantum Statistical Mechanics, vol. 2 (Springer, 1997)Google Scholar
  38. 38.
    S. Pironio, M. Navascués, A. Acín, SIAM J. Optim. 20(5), 2157 (2010). doi: 10.1137/090760155 MathSciNetCrossRefGoogle Scholar
  39. 39.
    A. Cabello, S. Severini, A. Winter (2010). arXiv:1010.2163
  40. 40.
    A. Cabello, S. Severini, A. Winter, Phys. Rev. Lett. 112, 040401 (2014). doi: 10.1103/PhysRevLett.112.040401 ADSCrossRefGoogle Scholar
  41. 41.
    L. Lovász, I.E.E.E. Trans, Inf. Theory 25, 1 (1979). doi: 10.1109/TIT.1979.1055985 CrossRefGoogle Scholar
  42. 42.
    L. Lovász, Geometric Representations of Graphs, (unpublished). www.cs.elte.hu/âlovasz/geomrep.pdf
  43. 43.
    S.L. Braunstein, C.M. Caves, Nucl. Phys. B, Proc. Suppl. 6, 211 (1989). doi: 10.1016/0920-5632(89)90441-6 Google Scholar
  44. 44.
    M. Reed, B. Simon, Methods of Modern Mathematical Physics, vol. I, (Academic Press, New York, 1972)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.University of SiegenSiegenGermany

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