Near-optimal and explicit Bell inequality violations

Harry Buhrman, Oded Regev, Giannicola Scarpa, Ronald De Wolf

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Bell inequality violations correspond to behavior of entangled quantum systems that cannot be simulated classically. We give two new two-player games with Bell inequality violations that are stronger, fully explicit, and arguably simpler than earlier work. The first game is based on the Hidden Matching problem of quantum communication complexity, introduced by Bar-Yossef, Jayram, and Kerenidis. This game can be won with probability 1 by a quantum strategy using a maximally entangled state with local dimension n (e.g., log n EPR-pairs), while we show that the winning probability of any classical strategy differs from 1/2 by at most O(log n√n). The second game is based on the integrality gap for Unique Games by Khot and Vishnoi and the quantum rounding procedure of Kempe, Regev, and Toner. Here n-dimensional entanglement allows to win the game with probability 1/(log n)2, while the best winning probability without entanglement is 1/n. This near-linear ratio ("Bell inequality violation") is near-optimal, both in terms of the local dimension of the entangled state, and in terms of the number of possible outputs of the two players.

Original languageEnglish (US)
Title of host publicationProceedings - 26th Annual IEEE Conference on Computational Complexity, CCC 2011
Pages157-166
Number of pages10
DOIs
StatePublished - 2011
Event26th Annual IEEE Conference on Computational Complexity, CCC 2011 - San Jose, CA, United States
Duration: Jun 8 2011Jun 10 2011

Publication series

NameProceedings of the Annual IEEE Conference on Computational Complexity
ISSN (Print)1093-0159

Other

Other26th Annual IEEE Conference on Computational Complexity, CCC 2011
CountryUnited States
CitySan Jose, CA
Period6/8/116/10/11

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Computational Mathematics

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  • Cite this

    Buhrman, H., Regev, O., Scarpa, G., & De Wolf, R. (2011). Near-optimal and explicit Bell inequality violations. In Proceedings - 26th Annual IEEE Conference on Computational Complexity, CCC 2011 (pp. 157-166). [5959805] (Proceedings of the Annual IEEE Conference on Computational Complexity). https://doi.org/10.1109/CCC.2011.30