An equivalence between time-symmetry and cyclic causality in quantum theory

• URL: http://arxiv.org/abs/2508.02463v1
• Date: Mon, 04 Aug 2025 14:30:46 GMT
• Title: An equivalence between time-symmetry and cyclic causality in quantum theory
• Authors: Eliot Jean, Ralph Silva, V. Vilasini,
• Abstract summary: We extend the P-CTC framework to define time-labelled P-CTC assisted combs.<n>We prove that for every (possibly mixed) MTS, there exists an operationally equivalent time-labelled P-CTC-assisted comb.<n>The equivalence is shown via explicit mappings, while discussing the number and dimensionality of the P-CTCs involved.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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