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Nonlocality beyond quantum mechanics

Abstract

Nonlocality is the most characteristic feature of quantum mechanics, but recent research seems to suggest the possible existence of nonlocal correlations stronger than those predicted by theory. This raises the question of whether nature is in fact more nonlocal than expected from quantum theory or, alternatively, whether there could be an as yet undiscovered principle limiting the strength of nonlocal correlations. Here, I review some of the recent directions in the intensive theoretical effort to answer this question.

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Figure 1: The black-box model of two experiments.

ANNA I. POPESCU

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References

  1. Aharonov, Y. & Bohm, D. Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485–491 (1959).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Bell, J. S. On the Einstein-Podolsky-Rosen paradox. Physics 1, 195–200 (1964).

    Article  MathSciNet  Google Scholar 

  3. Aharonov, Y. & Rohrlich, D. Quantum Paradoxes: Quantum Theory for the Perplexed (Wiley-VCH, 2005).

    Book  MATH  Google Scholar 

  4. Shimony, A. in Proc. Int. Symp. Foundations of Quantum Mechanics (eds Kamefuchi, S. et al.) 225–230 (Physical Society of Japan, 1983).

    Google Scholar 

  5. Popescu, S. & Rohrlich, D. Causality and non-locality as axioms for quantum mechanics. Found. Phys. 24, 379–385 (1994).

    Article  ADS  MathSciNet  Google Scholar 

  6. Horodecki, R., Horodecki, P., Horodecki, M. & Horodecki, K. Quantum entanglement. Rev. Mod. Phys. 81, 865–942 (2009). Extensive review of the characterization of quantum nonlocality.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Gisin, N. Bell inequality holds for all non-product states. Phys. Lett. A 154, 201–202 (1991).

    Article  ADS  MathSciNet  Google Scholar 

  8. Popescu, S. & Rohrlich, D. Generic quantum nonlocality. Phys. Lett. A 166, 293–297 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  9. Barrett, J., Collins, D., Hardy, L., Kent, A. & Popescu, S. Quantum nonlocality, Bell inequalities and the memory loophole. Phys. Rev. A 66, 42111 (2002).

    Article  ADS  Google Scholar 

  10. Brunner, N., Gisin, N. & Scarani, V. Entanglement and non-locality are different resources. New J. Phys. 7, 88 (2005).

    Article  ADS  Google Scholar 

  11. Cerf, N. J., Gisin, N., Massar, S. & Popescu, S. Simulating maximal quantum entanglement without communication. Phys. Rev. Lett. 94, 220403 (2005).

    Article  ADS  Google Scholar 

  12. Almeida, M., Pironio, S., Barrett, J., Tóth, G. & Acín, A. Noise robustness of the nonlocality of entangled quantum states. Phys. Rev. Lett. 99, 040403 (2007).

    Article  ADS  Google Scholar 

  13. Brunner, N., Gisin, N., Popescu, S. & Scarani, V. Simulation of partial entanglement with no-signaling resources. Phys. Rev. A 78, 52111 (2008).

    Article  ADS  Google Scholar 

  14. Allcock, J., Brunner, N., Pawlowski, M. & Scarani, V. Recovering part of the boundary between quantum and nonquantum correlations from information causality. Phys. Rev. A 80, 040103(R) (2009).

    Article  ADS  MathSciNet  Google Scholar 

  15. Acín, A. et al. Unified framework for correlations in terms of local quantum observables. Phys. Rev. Lett. 104, 140404 (2010).

    Article  ADS  Google Scholar 

  16. Barnum, H., Beigi, S., Boixo, S., Elliott, M. B. & Wehner, S. Local quantum measurement and no signaling imply quantum correlations. Phys. Rev. Lett. 104, 140401 (2010).

    Article  ADS  Google Scholar 

  17. Oppenheim, J. & Wehner, S. The uncertainty principle determines the nonlocality of quantum mechanics. Science 330, 1072–1074 (2010).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Barrett, J. & Gisin, N. How much measurement independence is needed to demonstrate nonlocality? Phys. Rev. Lett. 106, 100406 (2011).

    Article  ADS  Google Scholar 

  19. Gallego, R., Würflinger, L. E., Acín, A. & Navascués, M. Quantum correlations require multipartite information principles. Phys. Rev. Lett. 107, 210403 (2011).

    Article  ADS  Google Scholar 

  20. Bancal, J-D. et al. Quantum non-locality based on finite-speed causal influences leads to superluminal signalling. Nature Phys. 8, 867–870 (2012).

    Article  ADS  Google Scholar 

  21. Liang, Y-C., Masanes, L. & Rosset, D. All entangled states display some hidden nonlocality. Phys. Rev. A 86, 052115 (2012).

    Article  ADS  Google Scholar 

  22. Palazuelos, C. Superactivation of quantum nonlocality. Phys. Rev. Lett. 109, 190401 (2012).

    Article  ADS  Google Scholar 

  23. Vértesi, T. & Brunner, N. Quantum nonlocality does not imply entanglement distillability. Phys. Rev. Lett. 108, 030403 (2012).

    Article  ADS  Google Scholar 

  24. Cavalcanti, D., Acín, A., Brunner, N. & Vértesi, T. All quantum states useful for teleportation are nonlocal resources. Phys. Rev. A 87, 042104 (2013).

    Article  ADS  Google Scholar 

  25. Hirsch, F., Quintino, M. T., Bowles, J. & Brunner, N. Genuine hidden quantum nonlocality. Phys. Rev. Lett. 111, 160402 (2013).

    Article  ADS  Google Scholar 

  26. Khalfin, L. A. & Tsirelson, B. S. Quantum/classical correspondence in the light of Bell's inequalities. Found. Phys. 22, 879–948 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  27. Tsirelson, B. S. Some results and problems on quantum Bell-type inequalities. Hadronic J. Suppl. 8, 329–345 (1993).

    MathSciNet  MATH  Google Scholar 

  28. Tsirelson, B. S. Quantum analogues of the Bell inequalities. The case of two spatially separated domains. J. Sov. Math. 36, 557–570 (1987).

    Article  Google Scholar 

  29. Tsirelson, B. S. Quantum generalizations of Bell's inequality. Lett. Math. Phys. 4, 93–100 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  30. Navascués, M., Pironio, S. & Acín, A. Bounding the set of quantum correlations. Phys. Rev. Lett. 98, 10401 (2007).

    Article  ADS  Google Scholar 

  31. Navascués, M., Pironio, S. & Acín, A. A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations. New J. Phys. 10, 73013 (2008).

    Article  Google Scholar 

  32. Barnum, H., Barrett, J., Leifer, M. S. & Wilce, A. Generalized no-broadcasting theorem. Phys. Rev. Lett. 99, 240501 (2007).

    Article  ADS  Google Scholar 

  33. Barrett, J. Information processing in generalized probabilistic theories. Phys. Rev. A 75, 32304 (2007).

    Article  ADS  Google Scholar 

  34. Barrett, J. & Short, A. J. Strong non-locality: a tradeoff between states and measurements. New J. Phys. 12, 33034 (2010).

    Article  MathSciNet  Google Scholar 

  35. Barnum, H. et al. Entropy and information causality in general probabilistic theories. New J. Phys. 12, 033024 (2010).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. Short, A. J. & Wehner, S. Entropy in general physical theories. New J. Phys. 12, 33023 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  37. Gross, D., Mueller, M., Colbeck, R. & Dahlsten, O. C. O. All reversible dynamics in maximally nonlocal theories are trivial. Phys. Rev. Lett. 104, 80402 (2010).

    Article  ADS  Google Scholar 

  38. Janotta, P., Gogolin, C., Barrett, J. & Brunner, N. Limits on nonlocal correlations from the structure of the local state space. New J. Phys. 13, 063024 (2011).

    Article  ADS  Google Scholar 

  39. Barrett, J., Hardy, L. & Kent, A. No signaling and quantum key distribution. Phys. Rev. Lett. 95, 10503 (2005).

    Article  ADS  Google Scholar 

  40. Acín, A., Gisin, N. & Masanes, L. From Bell's theorem to secure quantum key distribution. Phys. Rev. Lett. 97, 120405 (2006).

    Article  ADS  MATH  Google Scholar 

  41. Scarani, V. et al. Secrecy extraction from no-signaling correlations. Phys. Rev. A 74, 42339 (2006).

    Article  ADS  Google Scholar 

  42. Acín, A. et al. Device-independent security of quantum cryptography against collective attacks. Phys. Rev. Lett. 98, 230501 (2007).

    Article  ADS  Google Scholar 

  43. Hänggi, E. & Renner, R. Device-independent quantum key distribution with commuting measurements. Preprint at http://arxiv.org/abs/1009.1833 (2010).

  44. Franz, T., Furrer, F. & Werner, R. F. Extremal quantum correlations and cryptographic security. Phys. Rev. Lett. 106, 250502 (2011).

    Article  ADS  Google Scholar 

  45. Masanes, L., Pironio, S. & Acín, A. Secure device independent quantum key distribution with causally independent measurement devices. Nature Commun. 2, 238 (2011).

    Article  ADS  Google Scholar 

  46. Barrett, J., Colbeck, R. & Kent, A. Unconditionally secure device-independent quantum key distribution with only two devices. Phys. Rev. A 86, 062326 (2012).

    Article  ADS  Google Scholar 

  47. Vazirani, U. & Vidick, T. Certifiable quantum dice. Phil. Trans. R. Soc. A. 370, 3432–3448 (2012).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. Barrett, J., Colbeck, R. & Kent, A. Memory attacks on device-independent quantum cryptography. Phys. Rev. Lett. 110, 010503 (2013).

    Article  ADS  Google Scholar 

  49. Huber, M. & Pawlowski, M. Weak randomness in device-independent quantum key distribution and the advantage of using high-dimensional entanglement. Phys. Rev. A 88, 032309 (2013).

    Article  ADS  Google Scholar 

  50. Colbeck, R. Quantum And Relativistic Protocols For Secure Multi-Party Computation PhD thesis, Univ. Cambridge (2007).

    Google Scholar 

  51. Pironio, S. et al. Random numbers certified by Bell's theorem. Nature 464, 1021–1024 (2010).

    Article  ADS  Google Scholar 

  52. Colbeck, R. & Kent, A. Private randomness expansion with untrusted devices. J. Phys. A 44, 095305 (2011).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  53. Acín, A., Massar, S. & Pironio, S. Randomness versus nonlocality and entanglement. Phys. Rev. Lett. 108, 100402 (2012).

    Article  ADS  Google Scholar 

  54. Colbeck, R. & Renner, R. Free randomness can be amplified. Nature Phys. 8, 450–454 (2012).

    Article  ADS  Google Scholar 

  55. Vazirani, U. & Vidick, T. in Proc. 44th Symp. Theory Comput. STOC 2012 (eds Pitassi, T. et al.) 61–76 (ACM Press, 2012).

    Google Scholar 

  56. Gallego, R. et al. Full randomness from arbitrarily deterministic events. Nature Commun. 4, 2654 (2013).

    Article  ADS  Google Scholar 

  57. Pironio, S. & Massar, S. Security of practical private randomness generation. Phys. Rev. A 87, 012336 (2013).

    Article  ADS  Google Scholar 

  58. Rabelo, R., Ho, M., Cavalcanti, D., Brunner, N. & Scarani, V. Device-independent certification of entangled measurements. Phys. Rev. Lett. 107, 050502 (2011).

    Article  ADS  Google Scholar 

  59. Bancal, J-D., Gisin, N., Liang, Y-C. & Pironio, S. Device-independent witnesses of genuine multipartite entanglement. Phys. Rev. Lett. 106, 250404 (2011).

    Article  ADS  Google Scholar 

  60. Moroder, T., Bancal, J-D., Liang, Y-C., Hofmann, M. & Gühne, O. Device-independent entanglement quantification and related applications. Phys. Rev. Lett. 111, 030501 (2013).

    Article  ADS  Google Scholar 

  61. Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V. & Wehner, S. Bell nonlocality. Preprint at http://arxiv.org/abs/1303.2849 (2013).

  62. Hardy, L. Quantum theory from five reasonable axioms. Preprint at http://arxiv.org/abs/quantph/0101012 (2001).

  63. Chiribella, G., D'Ariano, G. M. & Perinotti, P. Probabilistic theories with purification. Phys. Rev. A 81, 062348 (2010).

    Article  ADS  Google Scholar 

  64. Paterek, T., Dakić, B. & Brukner, C. Theories of systems with limited information content. New J. Phys. 12, 053037 (2010).

    Article  ADS  MATH  Google Scholar 

  65. Chiribella, G., D'Ariano, G. M. & Perinotti, P. Informational derivation of quantum theory. Phys. Rev. A 84, 012311 (2011).

    Article  ADS  Google Scholar 

  66. Masanes, L. & Müller, M. P. A derivation of quantum theory from physical requirements. New J. Phys. 13, 063001 (2011).

    Article  ADS  Google Scholar 

  67. de la Torre, G., Masanes, L., Short, A. J. & Müller, M. P. Deriving quantum theory from its local structure and reversibility. Phys. Rev. Lett. 109, 090403 (2012).

    Article  ADS  Google Scholar 

  68. Masanes, L., Müller, M. P., Augusiak, R. & Pérez-García, D. Existence of an information unit as a postulate of quantum theory. Proc. Natl Acad. Sci. USA. 110, 16373–16377 (2013).

    Article  ADS  Google Scholar 

  69. Müller, M. P. & Masanes, L. Three-dimensionality of space and the quantum bit: an information-theoretic approach. New J. Phys. 15, 053040 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  70. Popescu, S. Dynamical quantum non-locality. Nature Phys. 6, 151–153 (2010).

    Article  ADS  Google Scholar 

  71. Clauser, J. F., Horne, M. A., Shimony, A. & Holt, R. A. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880 (1969).

    Article  ADS  MATH  Google Scholar 

  72. Barrett, J., Linden, N., Massar, S., Pironio, S., Popescu, S. & Roberts, D. Non-local correlations as an information theoretic resource. Phys. Rev. A 71, 22101 (2005).

    Article  ADS  Google Scholar 

  73. van Dam, W. Implausible consequences of superstrong nonlocality. Preprint at http://arxiv.org/abs/quant-ph/0501159 (2005).

  74. Brassard, G. et al. Limit on nonlocality in any world in which communication complexity is not trivial. Phys. Rev. Lett. 96, 250401 (2006).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  75. Linden, N., Popescu, S., Short, A. J. & Winter, A. Quantum nonlocality and beyond: limits from nonlocal computation. Phys. Rev. Lett. 99, 180502 (2007).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  76. Pawlowski, M. et al. Information causality as a physical principle. Nature 461, 1101–1104 (2009).

    Article  ADS  Google Scholar 

  77. Navascués, M. & Wunderlich, H. A glance beyond the quantum model. Proc. R. Soc. A 466, 881–890 (2010).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  78. Fritz, T. et al. Local orthogonality as a multipartite principle for quantum correlations. Nature Commun. 4, 2263 (2013).

    Article  ADS  Google Scholar 

  79. Skrzypczyk, P., Brunner, N. & Popescu, S. Emergence of quantum correlations from nonlocality swapping. Phys. Rev. Lett. 102, 110402 (2009).

    Article  ADS  Google Scholar 

  80. Cleve, R., van Dam, W., Nielsen, M. & Tapp, A. Quantum Computing and Quantum Communication, Lecture Notes in Computer Science Vol. 1509 (Springer, 1999).

    MATH  Google Scholar 

  81. Cleve, R. & Buhrman, H. Substituting quantum entanglement for communication. Phys. Rev. A 56, 1201–1204 (1997).

    Article  ADS  Google Scholar 

  82. Barrett, J. & Pironio, S. Popescu-Rohrlich correlations as a unit of nonlocality. Phys. Rev. Lett. 95, 140401 (2005).

    Article  ADS  Google Scholar 

  83. Methot, A. A. & Scarani, V. An anomaly of nonlocality. Quantum Inform. Compu. 7, 157–170 (2007).

    MATH  Google Scholar 

  84. Forster, M., Winkler, S. & Wolf, S. Distilling nonlocality. Phys. Rev. Lett. 102, 120401 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  85. Brunner, N. & Skrzypczyk, P. Nonlocality distillation and postquantum theories with trivial communication complexity. Phys. Rev. Lett. 102, 160403 (2009).

    Article  ADS  Google Scholar 

  86. Pawlowski, M. & Brukner, C. Monogamy of Bell's inequality violations in nonsignaling theories. Phys. Rev. Lett. 102, 30403 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  87. Cavalcanti, D., Salles, A. & Scarani, V. Macroscopically local correlations can violate information causality. Nature Commun. 1, 136 (2010).

    Article  ADS  Google Scholar 

  88. Fitzi, M., Hänggi, E., Scarani, V. & Wolf, S. The nonlocality of n noisy Popescu–Rohrlich boxes. J. Phys. A 43, 465305 (2010).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  89. Brunner, N., Cavalcanti, D., Salles, A. & Skrzypczyk, P. Bound nonlocality and activation. Phys. Rev. Lett. 106, 20402 (2011).

    Article  ADS  Google Scholar 

  90. Gallego, R., Würflinger, L. E., Acín, A. & Navascués, M. Operational framework for nonlocality. Phys. Rev. Lett. 109, 70401 (2012).

    Article  ADS  Google Scholar 

  91. Borsten, L., Bradler, K. & Duff, M. J. Tsirelson's bound and supersymmetric entangled states. Preprint at http://arxiv.org/abs/1206.6934 (2012).

  92. Short, A. J., Popescu, S. & Gisin, N. Entanglement swapping for generalized nonlocal correlations. Phys. Rev. A 73, 12101 (2006).

    Article  ADS  Google Scholar 

  93. Branciard, C., Gisin, N. & Pironio, S. Characterizing the nonlocal correlations created via entanglement swapping. Phys. Rev. Lett. 104, 170401 (2010).

    Article  ADS  Google Scholar 

  94. Bancal, J-D., Brunner, N., Gisin, N. & Liang, Y-C. Detecting genuine multipartite quantum nonlocality: a simple approach and generalization to arbitrary dimensions. Phys. Rev. Lett. 106, 020405 (2011).

    Article  ADS  Google Scholar 

  95. Branciard, C., Rosset, D., Gisin, N. & Pironio, S. Bilocal versus nonbilocal correlations in entanglement swapping experiments. Phys. Rev. A 85, 032119 (2012).

    Article  ADS  Google Scholar 

  96. Bancal, J-D., Barrett, J., Gisin, N. & Pironio, S. Definitions of multipartite nonlocality. Phys. Rev. A 88, 014102 (2013).

    Article  ADS  Google Scholar 

  97. Gell-Mann, M. & Hartle, G. B. in Complexity, Entropy and the Physics of Information: SFI Studies in the Sciences of Complexity Vol VIII (ed. Zurek, W.) 150–173 (Addison Wesley, 1990).

    Google Scholar 

  98. Hartle, J. B. in Proc. 1992 Les Houches Summer School on Gravitation and Quantization (eds Zinn-Justin, J. & Julia, B.) 285–480 (North-Holland, 1995).

    Google Scholar 

  99. Sorkin, R. D. Quantum mechanics as quantum measure theory. Mod. Phys. Lett. A 9, 3119–3128 (1994).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  100. Dowker, F. Henson, J. & Wallden, P. A histories perspective on characterising quantum non-locality. Preprint at http://arxiv.org/abs/1311.6287 (2013).

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Popescu, S. Nonlocality beyond quantum mechanics. Nature Phys 10, 264–270 (2014). https://doi.org/10.1038/nphys2916

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