非局域游戏的锚定并行重复
量子物理
2021-03-09 v2 计算复杂性
摘要
我们引入一种对双玩家非局域游戏的简单变换，称为“锚定(anchoring)”，并证明了在量子纠缠玩家设定下所有锚定游戏的指数衰减并行重复定理。该变换部分受Feige-Kilian变换(SICOMP 2000)启发，并具有如下性质：若原游戏 的量子值为 ，则锚定游戏 的量子值为 ，其中 是变换的参数。特别地，锚定游戏量子值为 当且仅当原游戏 量子值为 。这为一般双玩家非局域游戏提供了首个实现量子值指数衰减的间隙放大技术。
引用
@article{arxiv.1509.07466,
title = {Anchored parallel repetition for nonlocal games},
author = {Mohammad Bavarian and Thomas Vidick and Henry Yuen},
journal= {arXiv preprint arXiv:1509.07466},
year = {2021}
}
备注
42 pages. Original version was published as "Hardness amplification for entangled games via anchoring" in the proceedings of Symposium on Theory of Computing 2017. This version is a revision to give more details on the proof of the quantum parallel repetition result. Classical multiplayer parallel repetition results no longer included, but can still be found in arXiv:1509.07466v1