论文标题
自我测试中的反例
Counterexamples in self-testing
论文作者
论文摘要
近年来，自我测试已发展成为一个丰富而活跃的研究领域，其应用从量子设备的实际验证到深度复杂性理论结果。自我测试允许经典的验证者推断出哪些量子测量值，以及在非本地游戏中使用的Alice Alice和Bob，例如使用哪种状态。因此，自我测试及其具有噪音的表亲（强大的自我测试）是非本地游戏的理想特征。 与人们的期望相反，我们对是否以及如何自我测试无法保持不完全了解。特别是，是否有一个具有量子优势的每个2方非本地游戏或贝尔不等式都证明了特定量子状态的存在？另外，是否可以通过足够的ingeniuty和努力使每个自我测试结果变得强大？我们通过提供简单且完全明确的反例来回答这些问题。为此，给定两个非局部游戏$ \ MATHCAL {G} _1 $和$ \ MATHCAL {G} _2 $，我们介绍了$（\ Mathcal {G} _1 \ lor \ Mathcal {G} _2 _2 _2）_2 _2 _2）$ - 游戏，在哪些玩家中可以播放哪些游戏，他们可以播放哪些游戏，他们可以选择游戏。如果玩家选择同一游戏并以他们给出的答案赢得比赛，则会获胜。我们的反例基于此游戏，我们认为这类游戏具有独立的兴趣。
In the recent years self-testing has grown into a rich and active area of study with applications ranging from practical verification of quantum devices to deep complexity theoretic results. Self-testing allows a classical verifier to deduce which quantum measurements and on what state are used, for example, by provers Alice and Bob in a nonlocal game. Hence, self-testing as well as its noise-tolerant cousin -- robust self-testing -- are desirable features for a nonlocal game to have. Contrary to what one might expect, we have a rather incomplete understanding of if and how self-testing could fail to hold. In particular, could it be that every 2-party nonlocal game or Bell inequality with a quantum advantage certifies the presence of a specific quantum state? Also, is it the case that every self-testing result can be turned robust with enough ingeniuty and effort? We answer these questions in the negative by providing simple and fully explicit counterexamples. To this end, given two nonlocal games $\mathcal{G}_1$ and $\mathcal{G}_2$, we introduce the $(\mathcal{G}_1 \lor \mathcal{G}_2)$-game, in which the players get pairs of questions and choose which game they want to play. The players win if they choose the same game and win it with the answers they have given. Our counterexamples are based on this game and we believe this class of games to be of independent interest.
