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Worst Case Analysis of Non-local Games

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Part of the Lecture Notes in Computer Science book series (LNTCS,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 x i to the i th player who then responds by sending an answer a i to the referee. The players win if the answers a i satisfy a condition that may depend on the inputs x i .

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.

Supported by ESF project 2009/0216/1DP/1.1.1.2.0/09/APIA/VIAA/044 and FP7 FET-Open project QCS.

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References

  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)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  3. Ambainis, A., Backurs, A., Balodis, K., Skuskovniks, A., Smotrovs, J., Virza, M.: Worst case analysis of non-local games

    Google Scholar 

  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)

    CrossRef  Google Scholar 

  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)

    MathSciNet  CrossRef  Google Scholar 

  6. Aravind, P.K.: The magic squares and Bell’s theorem (2002) (manuscript)

    Google Scholar 

  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. Briet, J., Vidick, T.: Explicit lower and upper bounds on the entangled value of multiplayer XOR games

    Google Scholar 

  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. Cirelson, B. (Tsirelson): Quantum generalizations of Bell’s inequality. Letters in Mathematical Physics 4, 93–100 (1980)

    MathSciNet  CrossRef  Google Scholar 

  11. Clauser, J., Horne, M., Shimony, A., Holt, R.: Proposed experiment to test local hidden-variable theories. Physical Review Letters 23, 880 (1969)

    CrossRef  Google Scholar 

  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. 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)

    CrossRef  Google Scholar 

  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. Merminm, D.: Extreme Quantum Entanglement in a Superposition of Macroscopically Distinct States. Physical Review Letters 65, 15 (1990)

    Google Scholar 

  16. Shor, P.W.: Algorithms for quantum computation: Discrete logarithms and factoring. In: FOCS 1994, pp. 124–134 (1994)

    Google Scholar 

  17. Silman, J., Chailloux, A., Aharon, N., Kerenidis, I., Pironio, S., Massar, S.: Fully distrustful quantum cryptography. Physical Review Letters 106, 220501 (2011)

    CrossRef  Google Scholar 

  18. Simon, D.R.: On the power of quantum computation. In: Proceedings of FOCS 1994, pp. 116–123. IEEE (1994)

    Google Scholar 

  19. Werner, R.F., Wolf, M.M.: Bell inequalities and Entanglement. Quantum Information and Computation 1(3), 1–25 (2001)

    MathSciNet  MATH  Google Scholar 

  20. de Wolf, R.: Quantum Communication and Complexity. Theoretical Computer Science 287(1), 337–353 (2002)

    MathSciNet  MATH  CrossRef  Google Scholar 

  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 

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Ambainis, A., Bačkurs, A., Balodis, K., Škuškovniks, A., Smotrovs, J., Virza, M. (2013). Worst Case Analysis of Non-local Games. In: van Emde Boas, P., Groen, F.C.A., Italiano, G.F., Nawrocki, J., Sack, H. (eds) SOFSEM 2013: Theory and Practice of Computer Science. SOFSEM 2013. Lecture Notes in Computer Science, vol 7741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35843-2_12

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  • DOI: https://doi.org/10.1007/978-3-642-35843-2_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35842-5

  • Online ISBN: 978-3-642-35843-2

  • eBook Packages: Computer ScienceComputer Science (R0)