A Superselection Rule for Quantum Causality

• URL: http://arxiv.org/abs/2508.17075v3
• Date: Mon, 15 Sep 2025 15:12:50 GMT
• Title: A Superselection Rule for Quantum Causality
• Authors: Issam Ibnouhsein,
• Abstract summary: Local laboratories are modeled as independent systems, each capable of implementing arbitrary instruments and selecting its own reference frames.<n>We elevate this symmetry to a fundamental principle for the resource-theoretic classification of quantum processes and demonstrate that, in the bipartite case, every covariant process is causally separable.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Within the process-matrix framework for quantum causality, local laboratories are modeled as independent systems, each capable of implementing arbitrary instruments and selecting its own reference frames. This operational freedom naturally induces a gauge symmetry in the connections between laboratories. We elevate this symmetry to a fundamental principle for the resource-theoretic classification of quantum processes and demonstrate that, in the bipartite case, every covariant process is causally separable. This theorem holds in arbitrary dimensions and applies both to marginals of multipartite quantum circuits and to general reductions across cuts. Since such covariance enforces a strict superselection rule, it provides a structural explanation for why all processes realizable within standard circuit frameworks-including the quantum switch-cannot violate bipartite causal inequalities, even in the asymptotic limit. Our analysis therefore establishes that generating nonclassical causal correlations requires physical resources that fundamentally break the operational independence of laboratories.

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