Correlation self-testing of a theory addresses the question of whether we can identify the set of correlations realisable in a theory from its performance in a particular information processing task. Applied to quantum theory it aims to identify an information processing task whose optimal performance is achieved only by theories realising the same correlations as quantum theory. In an accompanying paper we introduce a candidate task for this, the adaptive CHSH game. Here, we analyse the maximum probability of winning this game in different generalised probabilistic theories. We show that theories with a joint state space given by the minimal or the maximal tensor product are inferior to quantum theory, before considering other tensor products in theories whose elementary systems have various 2-dimensional state spaces. For these, we find no theories that outperform quantum theory in the adaptive CHSH game and prove that it is impossible to recover the quantum performance in various cases. This is the first step towards a general solution that, if successful, would have wide-ranging consequences, in particular, enabling an experiment that could rule out all theories in which the set of realisable correlations does not coincide with the quantum set.

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自适应Clauser-Horne-Shimony-Holt游戏中自测量子理论的可能性

理论的相关性自测试解决了以下问题：我们是否可以根据其在特定信息处理任务中的性能来确定理论中可实现的相关性集合。它应用于量子理论，旨在确定仅通过与量子理论实现相同相关性的理论来实现其最佳性能的信息处理任务。在随附的论文中，我们介绍了一个自适应CHSH游戏的候选任务。在这里，我们用不同的广义概率理论分析了赢得这场比赛的最大可能性。我们表明，在考虑基本系统具有各种二维状态空间的理论中的其他张量积之前，具有由最小或最大张量积给出的联合状态空间的理论不如量子理论。对于这些，我们没有发现在自适应CHSH博弈中能胜过量子理论的理论，并证明在各种情况下都不可能恢复量子性能。这是迈向通用解决方案的第一步，如果成功，它将产生广泛的后果，尤其是使实验能够排除所有可实现的相关性集与量子集不一致的理论。