Quantum guessing games form a versatile framework for studying different tasks of information processing. A quantum guessing game with posterior information uses quantum systems to encode messages and classical communication to give partial information after a quantum measurement has been performed. We present a general framework for quantum guessing games with posterior information and derive structure and reduction theorems that enable to analyze any such game. We formalize symmetry of guessing games and characterize the optimal measurements in cases where the symmetry is related to an irreducible representation. The application of guessing games to incompatibility detection is reviewed and clarified. All the presented main concepts and results are demonstrated with examples.

中文翻译：

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具有后验信息的量子猜谜游戏

量子猜谜游戏形成了一个多功能框架，用于研究不同的信息处理任务。具有后验信息的量子猜谜游戏使用量子系统对消息进行编码，并使用经典通信在执行量子测量后提供部分信息。我们为具有后验信息的量子猜谜游戏提出了一个通用框架，并推导出能够分析任何此类游戏的结构和缩减定理。我们将猜谜游戏的对称性形式化，并在对称性与不可约表示相关的情况下表征最佳测量。审查并阐明了猜谜游戏在不兼容性检测中的应用。所有提出的主要概念和结果都通过示例进行了演示。