As a quantum counterpart of labeled transition system (LTS), quantum labeled transition system (QLTS) is a powerful formalism for modeling quantum programs or protocols, and gives a categorical understanding for quantum computation. With the help of quantum branching monad, QLTS provides a framework extending some ideas in non-deterministic or probabilistic systems to quantum systems. On the other hand, quantum finite automata (QFA) emerged as a very elegant and simple model for resolving some quantum computational problems. In this paper, we propose the notion of reactive quantum system (RQS), a variant of QLTS capturing reactive system behavior, and develop a coalgebraic semantics for QLTS, RQS and QFA by an endofunctor on the category of convex sets, which has a final coalgebra. Such a coalgebraic semantics provides a unifying abstract interpretation for QLTS, RQS and QFA. The notions of bisimulation and simulation can be employed to compare the behavior of different types of quantum systems and judge whether a coalgebra can be behaviorally simulated by another.

中文翻译：

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量子系统的统一代数语义框架

作为标记转换系统（LTS）的量子对应物，量子标记转换系统（QLTS）是用于建模量子程序或协议的强大形式主义，并为量子计算提供了分类理解。在量子分支单子的帮助下，QLTS 提供了一个框架，将非确定性或概率系统中的一些想法扩展到量子系统。另一方面，量子有限自动机（QFA）作为一种非常优雅和简单的模型出现，用于解决一些量子计算问题。在本文中，我们提出了反应量子系统 (RQS) 的概念，这是 QLTS 捕获反应系统行为的一种变体，并通过凸集范畴上的内函子为 QLTS、RQS 和 QFA 开发了一种余代数语义，它具有最终的代数。这种代数语义为 QLTS、RQS 和 QFA 提供了统一的抽象解释。互模拟和模拟的概念可以用来比较不同类型量子系统的行为，并判断一个余代数是否可以被另一个在行为上模拟。