$A$和$B$形式的规范结构
Canonical structures of $A$ and $B$ forms
摘要：
在他们的开创性论文（Phys. Rev.121，920（1961））中，Sudarshan，Mathews和Rau研究了作用于$n$维量子系统的动态$A$和$B$映射的性质。开放量子系统演化中的动力学映射的性质近年来引起了人们的广泛关注。然而，关于$A$和$B$动态映射的新论文没有得到应有的重视。在这篇教程文章中，我们将回顾与有限维量子系统动力学相关的$A$和$B$形式的性质。特别是，我们调查了一个典型的结构与$A$形式，并建立其等价性与相关的$B$形式。我们表明，规范结构的$A$形式捕捉完全积极的（不完全积极的）性质的动态在一个简洁的方式。这一特点是通过量子位通道的物理例子来说明。
英文摘要：
In their seminal paper (Phys. Rev.121, 920 (1961)) Sudarshan, Mathews and Rau investigated properties of the dynamical $A$ and $B$ maps acting on $n$ dimensional quantum systems. Nature of the dynamical maps in open quantum system evolutions has attracted great deal of attention in the later years. However, the novel paper on the $A$ and $B$ dynamical maps has not received its due attention. In this tutorial article we review the properties of $A$ and $B$ forms associated with the dynamics of finite dimensional quantum systems. In particular we investigate a canonical structure associated with the $A$ form and establish its equivalence with the associated $B$ form. We show that the canonical structure of the $A$ form captures the completely positive (not completely positive) nature of the dynamics in a succinct manner. This feature is illustrated through physical examples of qubit channels.
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