Worst Case Analysis of Non-local Games

  • Andris Ambainis
  • Artūrs Bačkurs
  • Kaspars Balodis
  • Agnis Škuškovniks
  • Juris Smotrovs
  • Madars Virza
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7741)

Abstract

Non-local games are studied in quantum information because they provide a simple way for proving the difference between the classical world and the quantum world. A non-local game is a cooperative game played by 2 or more players against a referee. The players cannot communicate but may share common random bits or a common quantum state. A referee sends an input xi to the ith player who then responds by sending an answer ai to the referee. The players win if the answers ai satisfy a condition that may depend on the inputs xi.

Typically, non-local games are studied in a framework where the referee picks the inputs from a known probability distribution. We initiate the study of non-local games in a worst-case scenario when the referee’s probability distribution is unknown and study several non-local games in this scenario.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Acin, A., Brunner, N., Gisin, N., Massar, S., Pironio, S., Scarani, V.: Device-independent security of quantum cryptography against collective attacks. Physical Review Letters 98, 230501 (2007)CrossRefGoogle Scholar
  2. 2.
    Almeida, M.L., Bancal, J.-D., Brunner, N., Acin, A., Gisin, N., Pironio, S.: Guess your neighbour’s input: a multipartite non-local game with no quantum advantage. Physical Review Letters 104, 230404 (2010)CrossRefGoogle Scholar
  3. 3.
    Ambainis, A., Backurs, A., Balodis, K., Skuskovniks, A., Smotrovs, J., Virza, M.: Worst case analysis of non-local gamesGoogle Scholar
  4. 4.
    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
  5. 5.
    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
  6. 6.
    Aravind, P.K.: The magic squares and Bell’s theorem (2002) (manuscript)Google Scholar
  7. 7.
    Bennett, C.H., Brassard, G.: Quantum Cryptography: Public key distribution and coin tossing. In: Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, p. 175 (1984)Google Scholar
  8. 8.
    Briet, J., Vidick, T.: Explicit lower and upper bounds on the entangled value of multiplayer XOR gamesGoogle Scholar
  9. 9.
    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
  10. 10.
    Cirelson, B. (Tsirelson): Quantum generalizations of Bell’s inequality. Letters in Mathematical Physics 4, 93–100 (1980)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Clauser, J., Horne, M., Shimony, A., Holt, R.: Proposed experiment to test local hidden-variable theories. Physical Review Letters 23, 880 (1969)CrossRefGoogle Scholar
  12. 12.
    Cleve, R., Høyer, P., Toner, B., Watrous, J.: Consequences and limits of nonlocal strategies. In: Proceedings of CCC 2004, pp. 236–249 (2004)Google Scholar
  13. 13.
    Gavoille, C., Kosowski, A., Markiewicz, M.: What Can Be Observed Locally? In: Keidar, I. (ed.) DISC 2009. LNCS, vol. 5805, pp. 243–257. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  14. 14.
    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
  15. 15.
    Merminm, D.: Extreme Quantum Entanglement in a Superposition of Macroscopically Distinct States. Physical Review Letters 65, 15 (1990)Google Scholar
  16. 16.
    Shor, P.W.: Algorithms for quantum computation: Discrete logarithms and factoring. In: FOCS 1994, pp. 124–134 (1994)Google Scholar
  17. 17.
    Silman, J., Chailloux, A., Aharon, N., Kerenidis, I., Pironio, S., Massar, S.: Fully distrustful quantum cryptography. Physical Review Letters 106, 220501 (2011)CrossRefGoogle Scholar
  18. 18.
    Simon, D.R.: On the power of quantum computation. In: Proceedings of FOCS 1994, pp. 116–123. IEEE (1994)Google Scholar
  19. 19.
    Werner, R.F., Wolf, M.M.: Bell inequalities and Entanglement. Quantum Information and Computation 1(3), 1–25 (2001)MathSciNetMATHGoogle Scholar
  20. 20.
    de Wolf, R.: Quantum Communication and Complexity. Theoretical Computer Science 287(1), 337–353 (2002)MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Yao, A.: Probabilistic computations: Toward a unified measure of complexity. In: Proceedings of the 18th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 222–227 (1977)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Andris Ambainis
    • 1
  • Artūrs Bačkurs
    • 2
  • Kaspars Balodis
    • 1
  • Agnis Škuškovniks
    • 1
  • Juris Smotrovs
    • 1
  • Madars Virza
    • 2
  1. 1.Faculty of ComputingUniversity of LatviaRigaLatvia
  2. 2.Computer Science and Artificial Intelligence LaboratoryMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations