论文标题
量子可观察和仪器的组合
Combinations of Quantum Observables and Instruments
论文作者
论文摘要
本文指出，可观察和工具可以通过许多具有自然和物理解释的方式组合。我们将主要集中于这些组合的数学特性。 〜1节回顾了基本定义和可观察到的内容。我们研究可观察到的部分，后处理，广义凸组合，顺序产物和张量产物。这些组合扩展到〜3节中的仪器。我们考虑通过仪器组合测量的可观察到的特性。我们介绍了四种特殊类型的仪器，即克劳斯，吕德斯，琐碎和半繁琐的仪器。我们研究这些类型何时在各种组合下关闭。在这项工作中，我们仅考虑有限维量子系统。此处介绍的一些结果出现在作者之前的文章中。
This article points out that observables and instruments can be combined in many ways that have natural and physical interpretations. We shall mainly concentrate on the mathematical properties of these combinations. Section~1 reviews the basic definitions and observables are considered in Section~2. We study parts of observables, post-processing, generalized convex combinations, sequential products and tensor products. These combinations are extended to instruments in Section~3. We consider properties of observables measured by combinations of instruments. We introduce four special types of instruments, namely Kraus, Lüders, trivial and semitrivial instruments. We study when these types are closed under various combinations. In this work, we only consider finite-dimensional quantum systems. A few of the results presented here have appeared in the author's previous articles.
