Conditional distributions, as defined by the Markov category framework, are studied in the setting of matrix algebras (quantum systems). Their construction as linear unital maps are obtained via a categorical Bayesian inversion procedure. Simple criteria establishing when such linear maps are positive are obtained. Several examples are provided, including the standard EPR scenario, where the EPR correlations are reproduced in a purely compositional (categorical) manner. A comparison between the Bayes map and the Petz recovery map is provided, illustrating some key differences.

翻译：根据Markov类别框架的定义,在设置矩阵代数(量子系统)时研究条件分布,它们作为线性单线地图的构造是通过一个绝对的巴耶斯反向程序得出的,简单的标准是确定这种线性地图何时是正数,提供了几个例子,包括标准 EPR 设想方案,其中EPR 的关联纯粹以组成(分类)方式复制,提供了Bayes 地图和Petz 恢复地图之间的比较,说明了一些关键差异。