{"paper":{"title":"Single-letter Chain Rule for Quantum Relative Entropy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math-ph","math.IT","math.MP"],"primary_cat":"quant-ph","authors_text":"Giulio Gasbarri, Matt Hoogsteder-Riera","submitted_at":"2025-10-19T16:24:58Z","abstract_excerpt":"Relative entropy is the standard measure of distinguishability in classical and quantum information theory. In the classical case, its loss under channels admits an exact chain rule, while in the quantum case only asymptotic, regularized chain rules are known. We establish new chain rules for quantum relative entropy that apply already in the single-copy regime. The first inequality can be naturally obtained via POVM decompositions, extending the point distributions in the classical chain rule to quantum ensemble partitions. The second gives a sufficient condition for the most natural extensio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.16918","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.16918/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}