Operational Tube-Sector Theory of Quantum State Distinguishability Under Generalized Symmetries

• URL: http://arxiv.org/abs/2606.19678v2
• Date: Thu, 25 Jun 2026 10:15:52 GMT
• Title: Operational Tube-Sector Theory of Quantum State Distinguishability Under Generalized Symmetries
• Abstract summary: A variational principle for quantum-state distinguishability is established in many-body systems with generalized symmetries.<n>When symmetry actions terminate at entanglement cuts, distinguishability is governed by boundary tube algebras.<n>The resulting optimal measurement structure is uniquely fixed by the center of the boundary tube algebra.
• Score: 2.2003859300452198
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A variational principle for quantum-state distinguishability is established in many-body systems with generalized symmetries, including noninvertible cases described by fusion categories. Standard fidelity and symmetry-resolved diagnostics emerge as coarse-grained limits of a more refined operational structure. When symmetry actions terminate at entanglement cuts, distinguishability is governed by boundary tube algebras within a symmetry-constrained measurement resource theory. The physically admissible instruments are characterized by complete positivity, entanglement-cut locality, boundary-module covariance, and sequential stability. The resulting optimal measurement structure is uniquely fixed by the center of the boundary tube algebra, $\mathcal{A}_{\mathrm{phys}} = Z\!\left(\mathrm{Tube}_{\mathcal{C}}(\mathcal{M}_A)\right)$, whose primitive dempotents define tube-sector probabilities that refine fidelity-based and symmetry-resolved descriptions. The associated tube positive-operator-valued measures (POVMs) are extremal and yield optimal one-shot hypothesis-testing distinguishability under symmetry constraints. The categorical selection rule is universal across fusion categories and independent of microscopic realization; microscopic models enter by choosing the boundary module and the protocol family used to witness a nontrivial tube fiber.

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