An extension of Cencov's categorical description of classical inference theory to the domain of quantum systems is presented. It provides a novel categorical foundation to the theory of quantum information that embraces both classical and quantum information theory in a natural way, while also allowing to formalise the notion of quantum environment. A first application of these ideas is provided by extending the notion of statistical manifold to incorporate categories, and investigating a possible, uniparametric Cramer-Rao inequality in this setting.

翻译：本文提出了将Cencov关于经典推断理论的范畴化描述扩展到量子系统领域的方法。这为量子信息理论提供了新颖的范畴基础，既自然地涵盖了经典与量子信息理论，又允许对量子环境概念进行形式化表述。该思想的首个应用体现在将统计流形概念扩展以纳入范畴体系，并在此框架下探讨可能的单参数克拉美-罗不等式。