### 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 language | English (US) |
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Title of host publication | Proceedings - 26th Annual IEEE Conference on Computational Complexity, CCC 2011 |

Pages | 157-166 |

Number of pages | 10 |

DOIs | |

State | Published - 2011 |

Event | 26th Annual IEEE Conference on Computational Complexity, CCC 2011 - San Jose, CA, United States Duration: Jun 8 2011 → Jun 10 2011 |

### Other

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

Country | United States |

City | San Jose, CA |

Period | 6/8/11 → 6/10/11 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Computational Mathematics

### Cite this

*Proceedings - 26th Annual IEEE Conference on Computational Complexity, CCC 2011*(pp. 157-166). [5959805] https://doi.org/10.1109/CCC.2011.30

**Near-optimal and explicit Bell inequality violations.** / Buhrman, Harry; Regev, Oded; Scarpa, Giannicola; De Wolf, Ronald.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - 26th Annual IEEE Conference on Computational Complexity, CCC 2011.*, 5959805, pp. 157-166, 26th Annual IEEE Conference on Computational Complexity, CCC 2011, San Jose, CA, United States, 6/8/11. https://doi.org/10.1109/CCC.2011.30

}

TY - GEN

T1 - Near-optimal and explicit Bell inequality violations

AU - Buhrman, Harry

AU - Regev, Oded

AU - Scarpa, Giannicola

AU - De Wolf, Ronald

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.

UR - http://www.scopus.com/inward/record.url?scp=80051954966&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051954966&partnerID=8YFLogxK

U2 - 10.1109/CCC.2011.30

DO - 10.1109/CCC.2011.30

M3 - Conference contribution

SN - 9780769544113

SP - 157

EP - 166

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

ER -