{"paper":{"title":"Universal recovery maps and approximate sufficiency of quantum relative entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math-ph","math.IT","math.MP"],"primary_cat":"quant-ph","authors_text":"Andreas Winter, David Sutter, Marius Junge, Mark M. Wilde, Renato Renner","submitted_at":"2015-09-23T20:07:12Z","abstract_excerpt":"The data processing inequality states that the quantum relative entropy between two states $\\rho$ and $\\sigma$ can never increase by applying the same quantum channel $\\mathcal{N}$ to both states. This inequality can be strengthened with a remainder term in the form of a distance between $\\rho$ and the closest recovered state $(\\mathcal{R} \\circ \\mathcal{N})(\\rho)$, where $\\mathcal{R}$ is a recovery map with the property that $\\sigma = (\\mathcal{R} \\circ \\mathcal{N})(\\sigma)$. We show the existence of an explicit recovery map that is universal in the sense that it depends only on $\\sigma$ and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07127","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}