TY - GEN

T1 - Near-optimal and explicit Bell inequality violations

AU - Buhrman, Harry

AU - Regev, Oded

AU - Scarpa, Giannicola

AU - De Wolf, Ronald

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

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U2 - 10.1109/CCC.2011.30

DO - 10.1109/CCC.2011.30

M3 - Conference contribution

AN - SCOPUS:80051954966

SN - 9780769544113

T3 - Proceedings of the Annual IEEE Conference on Computational Complexity

SP - 157

EP - 166

BT - Proceedings - 26th Annual IEEE Conference on Computational Complexity, CCC 2011

T2 - 26th Annual IEEE Conference on Computational Complexity, CCC 2011

Y2 - 8 June 2011 through 10 June 2011

ER -