{"paper":{"title":"Reverse Test and Characterization of Quantum Relative Entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Keiji Matsumoto","submitted_at":"2010-10-05T21:52:23Z","abstract_excerpt":"The aim of the present paper is to give axiomatic characterization of quantum relative entropy utilizing resource conversion scenario. We consider two sets of axioms: non-asymptotic and asymptotic. In the former setting, we prove that the upperbound and the lowerbund of $\\mathrm{D}^{Q}(\\rho||\\sigma) $ is $\\mathrm{D}^{R}(\\rho||\\sigma) :=\\mathrm{tr}% \\,\\rho\\ln\\sqrt{\\rho}\\sigma^{-1}\\sqrt{\\rho}$ and $\\mathrm{D}(\\rho||\\sigma) :=$ $\\mathrm{tr}\\,\\rho(\\ln\\rho-\\ln\\sigma) $, respectively. In the latter setting, we prove uniqueness of quantum relative entropy, that is, $\\mathrm{D}^{Q}(\\rho||\\sigma) $ sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1030","kind":"arxiv","version":1},"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"}