research-article

Hardness amplification for entangled games via anchoring

Authors:

Mohammad Bavarian,

Henry YuenAuthors Info & Claims

STOC 2017: Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing

Pages 303 - 316

https://doi.org/10.1145/3055399.3055433

Published: 19 June 2017 Publication History

Abstract

We study the parallel repetition of one-round games involving players that can use quantum entanglement. A major open question in this area is whether parallel repetition reduces the entangled value of a game at an exponential rate - in other words, does an analogue of Raz's parallel repetition theorem hold for games with players sharing quantum entanglement? Previous results only apply to special classes of games.

We introduce a class of games we call anchored. We then introduce a simple transformation on games called anchoring, inspired in part by the Feige-Kilian transformation, that turns any (multiplayer) game into an anchored game. Unlike the Feige-Kilian transformation, our anchoring transformation is completeness preserving.

We prove an exponential-decay parallel repetition theorem for anchored games that involve any number of entangled players. We also prove a threshold version of our parallel repetition theorem for anchored games.

Together, our parallel repetition theorems and anchoring transformation provide the first hardness amplification techniques for general entangled games. We give an application to the games version of the Quantum PCP Conjecture.

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Index Terms

Hardness amplification for entangled games via anchoring
1. Theory of computation
  1. Computational complexity and cryptography
    1. Quantum complexity theory

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cover image ACM Conferences

STOC 2017: Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing

June 2017

1268 pages

ISBN:9781450345286

DOI:10.1145/3055399

General Chairs:
Hamed Hatami
McGill University
,
Pierre McKenzie
Université de Montréal
,
Program Chair:
Valerie King
University of Victoria

Copyright © 2017 ACM.

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Published: 19 June 2017

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https://doi.org/10.1007/s00023-024-01426-1
Kundu STan E(2023)Composably secure device-independent encryption with certified deletionQuantum10.22331/q-2023-07-06-10477(1047)Online publication date: 6-Jul-2023
https://doi.org/10.22331/q-2023-07-06-1047
Natarajan AZhang TSaha BServedio R(2023)Quantum Free GamesProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585208(1603-1616)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585208
Mousavi HNezhadi SYuen HLeonardi SGupta A(2022)Nonlocal games, compression theorems, and the arithmetical hierarchyProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3519949(1-11)Online publication date: 9-Jun-2022
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Jain RKundu S(2022)A direct product theorem for quantum communication complexity with applications to device-independent QKD2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS52979.2021.00125(1285-1295)Online publication date: Feb-2022
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Ji ZNatarajan AVidick TWright JYuen H(2021)MIP* = RECommunications of the ACM10.1145/348562864:11(131-138)Online publication date: 25-Oct-2021
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Jain RMiller CShi Y(2020)Parallel Device-Independent Quantum Key DistributionIEEE Transactions on Information Theory10.1109/TIT.2020.298674066:9(5567-5584)Online publication date: Sep-2020
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