论文标题
回顾的公理：与先验的时间反转对称性
Axioms for retrodiction: achieving time-reversal symmetry with a prior
论文作者
论文摘要
我们提出了一个类别的回顾理论定义，并使用它来展示所有量子通道的时间反转对称性。我们通过介绍回顾家族和函子来做到这一点，这些家族和函子捕获了许多直观的属性，这些直观的特性应满足，并且足够一般，可以涵盖经典和量子理论。古典贝叶斯倒置以及所有旋转和平均的佩茨恢复地图定义了回顾家庭。但是，平均旋转的PETZ恢复图，包括Junge-Renner-Sutter-Wilde-Winter的通用恢复图，由于无法满足某些组成性属性，因此不能定义回顾函数。在我们发现的所有示例中，最初的PETZ恢复图是唯一定义回顾函子的示例。此外，回顾函子表现出与量子理论的标准配方一致的推论时间反转对称性。这种回顾函子的存在似乎与量子通道的时间反转对称性上的许多无需结果形成鲜明对比。主要原因之一是因为这样的作品仅在量子通道的类别上定义了时间反转对称性，而我们将其定义为量子通道和量子状态的类别。这一事实进一步说明了先前的时间反转对称性的重要性。
We propose a category-theoretic definition of retrodiction and use it to exhibit a time-reversal symmetry for all quantum channels. We do this by introducing retrodiction families and functors, which capture many intuitive properties that retrodiction should satisfy and are general enough to encompass both classical and quantum theories alike. Classical Bayesian inversion and all rotated and averaged Petz recovery maps define retrodiction families in our sense. However, averaged rotated Petz recovery maps, including the universal recovery map of Junge-Renner-Sutter-Wilde-Winter, do not define retrodiction functors, since they fail to satisfy some compositionality properties. Among all the examples we found of retrodiction families, the original Petz recovery map is the only one that defines a retrodiction functor. In addition, retrodiction functors exhibit an inferential time-reversal symmetry consistent with the standard formulation of quantum theory. The existence of such a retrodiction functor seems to be in stark contrast to the many no-go results on time-reversal symmetry for quantum channels. One of the main reasons is because such works defined time-reversal symmetry on the category of quantum channels alone, whereas we define it on the category of quantum channels and quantum states. This fact further illustrates the importance of a prior in time-reversal symmetry.
