{"paper":{"title":"Reverse test and quantum analogue of classical fidelity and generalized fidelity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Keiji Matsumoto","submitted_at":"2010-06-02T05:46:33Z","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 D^{Q}({\\rho}||{\\sigma}) is D^{R}({\\rho}||{\\sigma}):=tr{\\rho}ln{\\sigma}^{1/2}{\\rho}^{-1}{\\sigma}^{1/2} and D({\\rho}||{\\sigma}):= tr{\\rho}(ln{\\rho}-ln{\\sigma}), respectively. In the latter setting, we prove uniqueness of quantum relative entropy, that is, D^{Q}({\\rho}||{\\sigma}) should equal a constant multiple of D({\\rho}||{\\sig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0302","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"}