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Natural Computing

, Volume 12, Issue 1, pp 9–12 | Cite as

Implausible consequences of superstrong nonlocality

  • Wim van Dam
Article

Abstract

We look at the consequences of so-called ‘superstrong nonlocal correlations’, which are hypothetical violations of Bell/CHSH inequalities that are stronger than quantum mechanics allows while still preventing the possibility of instantaneous communication. It is shown that the existence of maximally superstrong correlated bits implies that all distributed computations can be performed with a trivial amount of communication, i.e. with one bit. If one believes that Nature does not allow such a computational ‘free lunch’, then this result gives a reason why superstrong correlation are indeed not possible.

Keywords

Nonlocality Communication complexity Quantum information theory Foundations of quantum mechanics 

References

  1. Aspect A, Dalibard J, Roger G (1982) Experimental test of Bell’s inequalities using time-varying analyzers. Phys Rev Lett 49:1804–1807MathSciNetCrossRefGoogle Scholar
  2. Babai L, Frankl PG, Simon J (1986) Complexity classes in communication complexity theory. In: Proceedings of the 27th IEEE symposium on foundations of computer science. IEEE Computer Society Press, pp 337–347Google Scholar
  3. Bell JS (1964) On the Einstein-Podolsky-Rosen paradox. Physics 1:195–200Google Scholar
  4. Brassard G, Buhrman H, Linden N, Méthot AA, Tapp A, Unger F (2006) A limit on nonlocality in any world in which communication complexity is not trivial. Phys Rev Lett 96(25):250401. arXiv:quant-ph/0508042Google Scholar
  5. Cirel’son BS (1980) Quantum generalizations of Bell’s inequality. Lett Math Phys 4:93–100MathSciNetCrossRefGoogle Scholar
  6. Clauser JF, Horne MA, Shimony A, Holt RA (1969) Proposed experiment to test local hidden-variable theories. Phys Rev Lett 23:880–884CrossRefGoogle Scholar
  7. Cleve R, Buhrman H (1997) Substituting quantum entanglement for communication. Phys Rev A 56(2):1201–1204. arXiv:quant-ph/9704026Google Scholar
  8. Cleve R, van Dam W, Nielsen M, Tapp A (1998) Quantum entanglement and the communication complexity of the inner product function. In: Williams CP (ed) Proceedings of the first NASA international conference on quantum computing and quantum communications, vol 1509. Lecture Notes in Computer Science. Springer, pp 71–74. arXiv:quant-ph/9708019Google Scholar
  9. Freedman SJ, Clauser JF (1972) Experimental test of local hidden-variable theories. Phys Rev Lett 28:938–941CrossRefGoogle Scholar
  10. Kushilevitz E, Nisan N (1997) Communication complexity. Cambridge University Press, CambridgeMATHGoogle Scholar
  11. Popescu S, Rohrlich D (1994) Quantum nonlocality as an axiom. Found Phys 24(3):379–385MathSciNetCrossRefGoogle Scholar
  12. Popescu S, Rohrlich D (1997) The relativistic EPR argument. Potentiality, entanglement and passion-at-a-distance: quantum mechanical studies for Abner Shimony, vol 2. In: Cohen RS, Horne M, Stachel JJ (eds) Boston studies in the philosophy of science, vol. 194. Kluwer Academic Publishers. arXiv:quant-ph/9605004Google Scholar
  13. Rohrlich D, Popescu S (1996) Nonlocality as an axiom for quantum theory. In: Mann A, Revzen M (eds) The dilemma of Einstein, Podolsky and Rosen, 60 years later: international symposium in honour of Nathan Rosen. Annals of the Israel Physical Society, vol. 12. Israel Physical Society. arXiv:quant-ph/9508009Google Scholar
  14. van Dam W (2000) Nonlocality and communication complexity, Chap. 9. Ph.D. Thesis, University of OxfordGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Department of PhysicsUniversity of CaliforniaSanta BarbaraUSA

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