超越贝叶斯回溯的态检索
State retrieval beyond Bayes' retrodiction
AI总结：
该研究针对不可逆动力学中贝叶斯逆过程非最优的问题，基于态检索映射提出最优逆映射构建准则，发现贝叶斯逆映射是一类可优化选择的特例，该框架可推广至量子体系，且数值验证显示添加一条公理即可分离出贝叶斯逆过程。
摘要：
在不可逆动力学的背景下，为一个物理过程关联其直观的逆过程可能是一项相当模糊的任务。使用贝叶斯定理定义逆过程是一种标准选择，但总体而言，这种选择并非最优。在本研究中，我们探讨了是否有可能基于态检索映射的概念来刻画一种最优逆映射的构建。为此，我们提出了一组态检索映射应当满足的准则。我们发现，受贝叶斯启发的逆映射只是一整类可能选择中的一种情况，这类选择可以被优化，以得到一种比贝叶斯规则更精确地检索初始态的映射。我们的分析具备可自然推广至量子体系的优势。事实上，我们找到了一类逆变换，其中Petz恢复映射是一个特例，这佐证了将其解释为贝叶斯检索的量子类似物的观点。最后，我们给出了数值证据：通过添加一条额外公理，就可以分离出由贝叶斯定理推导而来的常规逆过程。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
