论文标题
连接XOR和XOR*游戏
Connecting XOR and XOR* games
论文作者
论文摘要
在这项工作中，我们专注于两类游戏：XOR非本地游戏和XOR*带有单分歧资源的顺序游戏。 XOR游戏已在非本地游戏的文献中进行了广泛的研究，我们将Xor* Games作为它们的自然游戏中的对应物，其中资源系统经过一系列受控操作和最终测量。 XOR*游戏的示例为$ 2 \ rightarrow 1 $量子随机访问代码（QRAC）和Henaut等人介绍的CHSH*游戏。在[PRA 98,060302（2018）]中。我们证明，使用过程理论的示意语言，在某些假设下，这两类游戏可以通过连接其最佳策略的显式定理相关，因此它们的经典（Bell）和Quantum（bell）和Quantum（Tsirelson）界限。我们还表明，在XOR* Games中，转换的可逆性和资源系统的双差异性 - 定理是通过提供明确的反例来保持的，这是必要的。我们以几个XOR/XOR*游戏对的示例结束，并通过详细讨论XOR*游戏中量子计算优势的可能资源。
In this work we focus on two classes of games: XOR nonlocal games and XOR* sequential games with monopartite resources. XOR games have been widely studied in the literature of nonlocal games, and we introduce XOR* games as their natural counterpart within the class of games where a resource system is subjected to a sequence of controlled operations and a final measurement. Examples of XOR* games are $2\rightarrow 1$ quantum random access codes (QRAC) and the CHSH* game introduced by Henaut et al. in [PRA 98,060302(2018)]. We prove, using the diagrammatic language of process theories, that under certain assumptions these two classes of games can be related via an explicit theorem that connects their optimal strategies, and so their classical (Bell) and quantum (Tsirelson) bounds. We also show that two of such assumptions -- the reversibility of transformations and the bi-dimensionality of the resource system in the XOR* games -- are strictly necessary for the theorem to hold by providing explicit counterexamples. We conclude with several examples of pairs of XOR/XOR* games and by discussing in detail the possible resources that power the quantum computational advantages in XOR* games.
