We provide a universal construction of the category of finite-dimensional C*-algebras and completely positive trace-nonincreasing maps from the rig category of finite-dimensional Hilbert spaces and unitaries. This construction, which can be applied to any dagger rig category, is described in three steps, each associated with their own universal property, and draws on results from dilation theory in finite dimension. In this way, we explicitly construct the category that captures hybrid quantum/classical computation with possible nontermination from the category of its reversible foundations. We discuss how this construction can be used in the design and semantics of quantum programming languages.

翻译：我们提供了从有限维希尔伯特空间与酉算子的刚性范畴到有限维C*-代数与完全正迹非增映射范畴的普适构造。该构造可应用于任意dagger刚性范畴，通过三个步骤实现，每一步均关联其自身的普适性质，并借鉴了有限维膨胀理论的研究成果。通过这种方式，我们明确地从可逆基础范畴构造了捕捉混合量子/经典计算（可能包含非终止性）的范畴。本文讨论了该构造在量子编程语言设计与语义中的应用。