{"paper":{"title":"Recovery map stability for the Data Processing Inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.OA","authors_text":"Anna Vershynina, Eric A. Carlen","submitted_at":"2017-10-06T13:58:56Z","abstract_excerpt":"The Data Processing Inequality (DPI) says that the Umegaki relative entropy $S(\\rho||\\sigma) := {\\rm Tr}[\\rho(\\log \\rho - \\log \\sigma)]$ is non-increasing under the action of completely positive trace preserving (CPTP) maps. Let ${\\mathcal M}$ be a finite dimensional von Neumann algebra and ${\\mathcal N}$ a von Neumann subalgebra if it. Let ${\\mathcal E}_\\tau$ be the tracial conditional expectation from ${\\mathcal M}$ onto ${\\mathcal N}$. For density matrices $\\rho$ and $\\sigma$ in ${\\mathcal N}$, let $\\rho_{\\mathcal N} := {\\mathcal E}_\\tau \\rho$ and $\\sigma_{\\mathcal N} := {\\mathcal E}_\\tau \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02409","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"}