{"paper":{"title":"On extension of quantum channels and operations to the space of relatively bounded operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP","math.OA","quant-ph"],"primary_cat":"math-ph","authors_text":"M.E.Shirokov","submitted_at":"2019-03-14T15:45:13Z","abstract_excerpt":"We analyse possibility to extend a quantum operation (sub-unital normal CP linear map on the algebra $B(H)$ of bounded operators on a separable Hilbert space $H$) to the space of all operators on $H$ relatively bounded w.r.t. a given positive unbounded operator.\n  We show that a quantum operation $\\,\\Phi\\,$ can be uniquely extended to a bounded linear operator on the Banach space of all $\\sqrt{G}$-bounded operators on $H$ provided that the operation $\\Phi$ is $G$-limited: the predual operation $\\Phi_*$ maps the set of positive trace class operators $\\rho$ with finite $\\mathrm{Tr}\\rho G$ into i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06086","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1903.06086/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}