论文标题
州检索超出贝叶斯的改编
State retrieval beyond Bayes' retrodiction
论文作者
论文摘要
在不可逆转的动态的背景下，与物理过程相关联，其直观的反向可能导致一项非常模棱两可的任务。它是使用贝叶斯定理定义反向过程的标准选择，但总的来说，此选择并不是最佳选择。在这项工作中，我们探索是否可以从状态检索地图的概念中表征最佳的反向映射。通过这样做，我们提出了一组原则，即州检索地图应该满足。我们发现，受贝叶斯启发的反向只是一类可能的选择中的一种情况，可以优化以比贝叶斯规则更精确地获得初始状态的地图。我们的分析具有自然扩展到量子状态的优势。实际上，我们发现一类包含PETZ恢复图的反向转换是一种特定的情况，证实了其解释为贝叶斯检索的量子类似物。最后，我们提出了数值证据，即通过添加单个额外的公理可以隔离贝叶斯定理的通常反向过程。
In the context of irreversible dynamics, associating to a physical process its intuitive reverse can result to be a quite ambiguous task. It is a standard choice to define the reverse process using Bayes' theorem, but, in general, this choice is not optimal. In this work we explore whether it is possible to characterise an optimal reverse map building from the concept of state retrieval maps. In doing so, we propose a set of principles that state retrieval maps should satisfy. We find out that the Bayes inspired reverse is just one case in a whole class of possible choices, which can be optimised to give a map retrieving the initial state more precisely than the Bayes rule. Our analysis has the advantage of naturally extending to the quantum regime. In fact, we find a class of reverse transformations containing the Petz recovery map as a particular case, corroborating its interpretation as quantum analogue of the Bayes retrieval. Finally, we present numerical evidences that by adding a single extra axiom one can isolate the usual reverse process derived from Bayes' theorem.
