{"paper":{"title":"Note on a Family of Monotone Quantum Relative Entropies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Andreas Deuchert, Christian Hainzl, Robert Seiringer","submitted_at":"2015-02-25T15:39:32Z","abstract_excerpt":"Given a convex function $\\varphi$ and two hermitian matrices $A$ and $B$, Lewin and Sabin study in [M. Lewin, J. Sabin, {\\it A Family of Monotone Quantum Relative Entropies}, Lett. Math. Phys. \\textbf{104} (2014), 691-705.] the relative entropy defined by $\\mathcal{H}(A,B)=\\text{Tr} [ \\varphi(A) - \\varphi(B) - \\varphi'(B)(A-B) ]$. Amongst other things, they prove that the so-defined quantity is monotone if and only if $\\varphi'$ is operator monotone. The monotonicity is then used to properly define $\\mathcal{H}(A,B)$ for self-adjoint bounded operators acting on an infinite-dimensional Hilbert "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07205","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"}