{"paper":{"title":"Lower semicontinuity of the entropic disturbance and its applications in quantum information theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"A.S. Holevo, M.E. Shirokov","submitted_at":"2016-08-07T11:37:02Z","abstract_excerpt":"We prove that for any infinite-dimensional quantum channel the entropic disturbance (defined as difference between the $\\chi$-quantity of a generalized ensemble and that of the image of the ensemble under the channel) is lower semicontinuous on the natural set of its definition. We establish a number of useful corollaries of this property, in particular, we prove the continuity of the output $\\chi\\textrm{-}$quantity and the existence of $\\chi$-optimal ensemble for any quantum channel under the energy-type input constraint."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02203","kind":"arxiv","version":2},"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"}