2025/08/04 by Eliot Jean, Ralph Silva, Jean, Eliot +3
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2508.02463
openalex publication_date 2025/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.