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, the Petz recovery map, and the Leifer-Spekkens acausal belief propagation is provided, illustrating some similarities and key differences.

翻译：在设置矩阵代数(量子系统)时研究Markov类别框架界定的有条件分布,它们作为线性单位图的构造是通过一个绝对的巴伊西亚反向程序得出的,简单的标准是确定这种线性地图何时为正数,提供了几个例子,包括标准 EPR 设想,即EPR 相关关系纯粹以组成(分类)方式复制。提供了Bayes 地图、Petz 恢复地图和Leifer-Spekkkens causal信仰传播的比较,说明了一些相似之处和关键差异。