论文标题
从时间反转对称到量子贝叶斯的规则
From time-reversal symmetry to quantum Bayes' rules
论文作者
论文摘要
贝叶斯的规则$ \ MATHBB {p}（b | a）\ MATHBB {p}（a）= \ Mathbb {p}（a | b）\ Mathbb {p}（b）$是最简单，最深刻，最无用的，无处不在的，且无处不在，并且是经典的概率和远程范围的结果，这些结果涉及任何领域，并在任何领域中都在任何领域的应用。已经尝试将此规则扩展到量子系统，我们才开始理解其意义。在这项工作中，我们开发了一个系统的框架，用于在量子环境中定义贝叶斯的规则，并且我们表明，在文献中出现的绝大多数拟议的量子贝叶斯规则都是我们定义的实例。此外，我们的贝叶斯规则是基于随着时间的流逝的状态概念与时间反转对称图之间的简单关系，这两者都在此处介绍。
Bayes' rule $\mathbb{P}(B|A)\mathbb{P}(A)=\mathbb{P}(A|B)\mathbb{P}(B)$ is one of the simplest yet most profound, ubiquitous, and far-reaching results of classical probability theory, with applications in any field utilizing statistical inference. Many attempts have been made to extend this rule to quantum systems, the significance of which we are only beginning to understand. In this work, we develop a systematic framework for defining Bayes' rule in the quantum setting, and we show that a vast majority of the proposed quantum Bayes' rules appearing in the literature are all instances of our definition. Moreover, our Bayes' rule is based upon a simple relationship between the notions of state over time and a time-reversal symmetry map, both of which are introduced here.
