{"paper":{"title":"On a quantum version of Shannon's conditional entropy","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Robert Schrader","submitted_at":"2000-03-14T17:29:51Z","abstract_excerpt":"In this article we propose a quantum version of Shannon's conditional entropy. Given two density matrices $\\rho$ and $\\sigma$ on a finite dimensional Hilbert space and with $S(\\rho)=-\\tr\\rho\\ln\\rho$ being the usual von Neumann entropy, this quantity $S(\\rho|\\sigma)$ is concave in $\\rho$ and satisfies $0\\le S(\\rho|\\sigma)\\le S(\\rho)$, a quantum analogue of Shannon's famous inequality. Thus we view $S(\\rho|\\sigma)$ as the entropy of $\\rho$ conditioned by $\\sigma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0003048","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"}