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Nonlocal Quantum XOR Games for Large Number of Players

  • Andris Ambainis
  • Dmitry Kravchenko
  • Nikolajs Nahimovs
  • Alexander Rivosh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6108)

Abstract

Nonlocal games are used to display differences between classical and quantum world. In this paper, we study nonlocal games with a large number of players. We give simple methods for calculating the classical and the quantum values for symmetric XOR games with one-bit input per player, a subclass of nonlocal games. We illustrate those methods on the example of the N-player game (due to Ardehali [Ard92]) that provides the maximum quantum-over-classical advantage.

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References

  1. [Ard92]
    Ardehali, M.: Bell inequalities with a magnitude of violation that grows exponentially with the number of particles. Physical Review A 46, 5375–5378 (1992)CrossRefMathSciNetGoogle Scholar
  2. [CHSH69]
    Clauser, J., Horne, M., Shimony, A., Holt, R.: Phys. Rev. Lett. 23, 880 (1969)Google Scholar
  3. [CHTW04]
    Cleve, R., Høyer, P., Toner, B., Watrous, J.: Consequences and limits of nonlocal strategies. In: Proceedings of the 19th IEEE Conference on Computational Complexity (CCC 2004), pp. 236–249 (2004)Google Scholar
  4. [Cir80]
    Tsirelson, B.S.: Quantum generalizations of Bell’s inequality. Letters in Mathematical Physics 4(2), 93–100 (1980)CrossRefMathSciNetGoogle Scholar
  5. [Kem08]
    Kempe, J., Kobayashi, H., Matsumoto, K., Toner, B., Vidick, T.: Entangled Games are Hard to Approximate. In: Proceedings of FOCS 2008, pp. 447–456 (2008)Google Scholar
  6. [Mer90]
    Mermin, D.: Extreme Quantum Entanglement in a Superposition of Macroscopically Distinct States. Physical Review Letters 65, 15 (1990)Google Scholar
  7. [PW+08]
    Perez-Garcia, D., Wolf, M.M., Palazuelos, C., Villanueva, I., Junge, M.: Unbounded violation of tripartite Bell inequalities. Communications in Mathematical Physics 279, 455 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  8. [WW01]
    Werner, R.F., Wolf, M.M.: Bell inequalities and Entanglement. Quant. Inf. Comp. 1(3), 1–25 (2001)zbMATHMathSciNetGoogle Scholar
  9. [WW01a]
    Werner, R.F., Wolf, M.M.: All multipartite Bell correlation inequalities for two dichotomic observables per site. Phys. Rev. A 64, 032112 (2001)CrossRefGoogle Scholar
  10. [ZB02]
    Zukowski, M., Bruckner, C.: Bell’s theorem for general N-qubit states. Phys. Rev. Lett. 88, 210401 (2002)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Andris Ambainis
    • 1
  • Dmitry Kravchenko
    • 1
  • Nikolajs Nahimovs
    • 1
  • Alexander Rivosh
    • 1
  1. 1.Faculty of ComputingUniversity of Latvia 

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