论文标题
量子马尔可夫类别中的逆，瓦解和贝叶斯倒置
Inverses, disintegrations, and Bayesian inversion in quantum Markov categories
论文作者
论文摘要
我们将量子马尔可夫类别介绍为一种结构，该结构可以完善并扩展概率理论和信息理论的合成方法，从而包括量子概率和量子信息理论。在这种更广泛的背景下，我们分析了三个依次的可逆性和统计推断的更一般的概念：普通的倒置，分解和贝叶斯倒置。我们证明，每个子类别都是后者的严格特殊实例，为贝叶斯倒置提供了分类的基础，以此作为逆转过程的概括。我们统一了几乎所有（A.E.）等价的分类和$ C^*$ - 代数概念。结果，我们证明了许多结果，包括针对S阳性类别的通用的No-broadcast定理，S阳性类别是A.E.模块化类别，错误纠正代码和崩解之间的关系以及贝叶斯倒置与叶umegaki的非交通充足性之间的关系。
We introduce quantum Markov categories as a structure that refines and extends a synthetic approach to probability theory and information theory so that it includes quantum probability and quantum information theory. In this broader context, we analyze three successively more general notions of reversibility and statistical inference: ordinary inverses, disintegrations, and Bayesian inverses. We prove that each one is a strictly special instance of the latter for certain subcategories, providing a categorical foundation for Bayesian inversion as a generalization of reversing a process. We unify the categorical and $C^*$-algebraic notions of almost everywhere (a.e.) equivalence. As a consequence, we prove many results including a universal no-broadcasting theorem for S-positive categories, a generalized Fisher--Neyman factorization theorem for a.e. modular categories, a relationship between error correcting codes and disintegrations, and the relationship between Bayesian inversion and Umegaki's non-commutative sufficiency.
