Advantage of Quantum Strategies in Random Symmetric XOR Games

  • Andris Ambainis
  • Jānis Iraids
  • Dmitry Kravchenko
  • Madars Virza
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7721)

Abstract

Non-local games are known as a simple but useful model which is widely used for displaying nonlocal properties of quantum mechanics. In this paper we concentrate on a simple subset of non-local games: multiplayer XOR games with 1-bit inputs and 1-bit outputs which are symmetric w.r.t. permutations of players.

We look at random instances of non-local games from this class. We prove a tight bound for the expected performance on the classical strategies for a random non-local game and provide numerical evidence that quantum strategies achieve better results.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [ABB+12]
    Ambainis, A., Bačkurs, A., Balodis, K., Kravčenko, D., Ozols, R., Smotrovs, J., Virza, M.: Quantum Strategies Are Better Than Classical in Almost Any XOR Game. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012. LNCS, vol. 7391, pp. 25–37. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  2. [AKNR09]
    Ambainis, A., Kravchenko, D., Nahimovs, N., Rivosh, A.: Nonlocal Quantum XOR Games for Large Number of Players. In: Kratochvíl, J., Li, A., Fiala, J., Kolman, P. (eds.) TAMC 2010. LNCS, vol. 6108, pp. 72–83. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. [Ar92]
    Ardehali, M.: Bell inequalities with a magnitude of violation that grows exponentially with the number of particles. Physical Review A 46, 5375–5378 (1992)MathSciNetCrossRefGoogle Scholar
  4. [Be64]
    Bell, J.: On the Einstein-Podolsky-Rosen paradox. Physics 1(3), 195–200 (1964)Google Scholar
  5. [BV11]
    Briët, J., Vidick, T.: Explicit lower and upper bounds on the entangled value of multiplayer XOR games. arXiv:1108.5647Google Scholar
  6. [BRSW11]
    Buhrman, H., Regev, O., Scarpa, G., de Wolf, R.: Near-Optimal and Explicit Bell Inequality Violations. In: Proceedings of CCC 2011, pp. 157–166 (2011)Google Scholar
  7. [CHSH69]
    Clauser, J., Horne, M., Shimony, A., Holt, R.: Physical Review Letters 23, 880 (1969)CrossRefGoogle Scholar
  8. [CHTW04]
    Cleve, R., Høyer, P., Toner, B., Watrous, J.: Consequences and limits of nonlocal strategies. In: Proceedings of CCC 2004, pp. 236–249 (2004); Also quant-ph/0404076Google Scholar
  9. [Kr01]
    Krasikov, I.: Nonnegative Quadratic Forms and Bounds on Orthogonal Polynomials. Journal of Approximation Theory 111, 31–49 (2001), doi:10.1006/jath.2001.3570MathSciNetMATHCrossRefGoogle Scholar
  10. [Me90]
    Mermin, D.: Extreme Quantum Entanglement in a Superposition of Macroscopically Distinct States. Physical Review Letters 65(15) (1990)Google Scholar
  11. [SZ54]
    Salem, R., Zygmund, A.: Some properties of trigonometric series whose terms have random signs. Acta Math. 91, 245–301 (1954)MathSciNetMATHCrossRefGoogle Scholar
  12. [WW01]
    Werner, R.F., Wolf, M.M.: Bell inequalities and Entanglement. Quantum Information and Computation 1(3), 1–25 (2001)MathSciNetMATHGoogle Scholar
  13. [WW01a]
    Werner, R.F., Wolf, M.M.: All multipartite Bell correlation inequalities for two dichotomic observables per site. Physical Review A 64, 32112 (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Andris Ambainis
    • 1
  • Jānis Iraids
    • 1
  • Dmitry Kravchenko
    • 1
  • Madars Virza
    • 1
  1. 1.Faculty of ComputingUniversity of LatviaLatvia

Personalised recommendations