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2011 26th Annual IEEE Conference on Computational Complexity
Near-Optimal and Explicit Bell Inequality Violations
San Jose, California USA
June 08-June 11
ISBN: 978-0-7695-4411-3
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:
Harry Buhrman, Oded Regev, Giannicola Scarpa, Ronald de Wolf, "Near-Optimal and Explicit Bell Inequality Violations," ccc, pp.157-166, 2011 26th Annual IEEE Conference on Computational Complexity, 2011
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