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.
Similar content being viewed by others
References
Aspect A, Dalibard J, Roger G (1982) Experimental test of Bell’s inequalities using time-varying analyzers. Phys Rev Lett 49:1804–1807
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 337–347
Bell JS (1964) On the Einstein-Podolsky-Rosen paradox. Physics 1:195–200
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/0508042
Cirel’son BS (1980) Quantum generalizations of Bell’s inequality. Lett Math Phys 4:93–100
Clauser JF, Horne MA, Shimony A, Holt RA (1969) Proposed experiment to test local hidden-variable theories. Phys Rev Lett 23:880–884
Cleve R, Buhrman H (1997) Substituting quantum entanglement for communication. Phys Rev A 56(2):1201–1204. arXiv:quant-ph/9704026
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/9708019
Freedman SJ, Clauser JF (1972) Experimental test of local hidden-variable theories. Phys Rev Lett 28:938–941
Kushilevitz E, Nisan N (1997) Communication complexity. Cambridge University Press, Cambridge
Popescu S, Rohrlich D (1994) Quantum nonlocality as an axiom. Found Phys 24(3):379–385
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/9605004
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/9508009
van Dam W (2000) Nonlocality and communication complexity, Chap. 9. Ph.D. Thesis, University of Oxford
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
van Dam, W. Implausible consequences of superstrong nonlocality. Nat Comput 12, 9–12 (2013). https://doi.org/10.1007/s11047-012-9353-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11047-012-9353-6