2011 IEEE 26th Annual Conference on Computational Complexity (2011)

San Jose, California USA

June 8, 2011 to June 11, 2011

ISSN: 1093-0159

ISBN: 978-0-7695-4411-3

pp: 157-166

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/CCC.2011.30

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)/sqrt(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.

INDEX TERMS

quantum computing, nonlocal games, Bell inequality, communication complexity

CITATION

G. Scarpa, H. Buhrman, R. de Wolf and O. Regev, "Near-Optimal and Explicit Bell Inequality Violations,"

*2011 IEEE 26th Annual Conference on Computational Complexity(CCC)*, San Jose, California USA, 2011, pp. 157-166.

doi:10.1109/CCC.2011.30

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