量子理论中时间对称性与循环因果性的等价性
An equivalence between time-symmetry and cyclic causality in quantum theory
AI总结：
该研究针对量子基础中时间对称性与因果方向性的关联问题，扩展P-CTC框架定义带时间标记的P-CTC辅助梳，证明其与多时间态MTS操作等价，并探讨了MTS的资源理论偏序与未来研究方向。
摘要：
理解物理定律的时间对称本质与因果性的表观方向性之间的关系，是量子基础研究中的一个核心问题。量子信息领域广泛使用的标准操作表述，为智能体的操作施加了确定的非循环因果顺序，这与时间对称的动力学形成了对比。该框架的两个重要扩展分别是多时间态（multi-time state, MTS）形式体系和后选择闭合类时曲线（post-selected closed timelike curve, P-CTC）框架：前者通过任意的前选择与后选择纳入了时间对称性，后者则通过对最大纠缠态进行后选择实现了循环因果影响。尽管已有研究注意到MTS与P-CTC之间的结构关联，但二者是否存在操作等价性，以及能否在其最广义的对象之间建立构造性映射，仍未明确。在本工作中，我们通过扩展P-CTC框架定义了带时间标记的P-CTC辅助梳（time-labelled P-CTC assisted combs）——这是一类更具一般性的P-CTC辅助对象，支持开放处理槽和显式时间结构——从而填补了这一空白。我们证明，对于每一个（可能是混态的）MTS，都存在一个操作上等价的带时间标记的P-CTC辅助梳，反之亦然。我们通过显式映射证明了这一等价性，同时讨论了所涉及的P-CTC的数量和维度。我们还从资源理论的视角探讨了MTS，定义了在不使用P-CTC的自由变换下的偏序关系。最后，我们基于本文建立的时间对称性与循环因果性之间的操作等价性，讨论了未来的研究方向。
英文摘要：
Understanding the relationship between the time-symmetric nature of physical laws and the apparent directionality of causality is a central question in quantum foundations. The standard operational formulation, widely used in quantum information, imposes a definite, acyclic causal order on agents' operations, contrasting with time-symmetric dynamics. Two prominent extensions of this framework are the multi-time state (MTS) formalism, which incorporates time symmetry via arbitrary pre- and post-selection, and the post-selected closed timelike curve (P-CTC) framework, which enables cyclic causal influences through post-selection on maximally entangled states. While prior work has noted structural connections between MTS and P-CTCs, it remained unclear whether an operational equivalence exists, or whether constructive mappings can be established between their most general objects. In this work, we address this gap by extending the P-CTC framework to define time-labelled P-CTC assisted combs, a more general class of P-CTC-assisted objects that support open processing slots and explicit temporal structure. We prove that for every (possibly mixed) MTS, there exists an operationally equivalent time-labelled P-CTC-assisted comb, and vice versa. The equivalence is shown via explicit mappings, while discussing the number and dimensionality of the P-CTCs involved. We also explore a resource-theoretic view of MTS, defining a partial order under free transformations that do not use P-CTCs. We conclude by discussing future directions informed by the operational equivalence between time symmetry and cyclic causality established here.
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