{"paper":{"title":"On completion of the cone of CP linear maps with respect to the energy-constrained diamond norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OA","quant-ph"],"primary_cat":"math.FA","authors_text":"M.E.Shirokov","submitted_at":"2018-10-25T15:20:50Z","abstract_excerpt":"For a given positive operator $G$ we consider the cones of linear maps between Banach spaces of trace class operators characterized by the Stinespring-like representation with $\\sqrt{G}$-bounded and $\\sqrt{G}$-infinitesimal operators correspondingly. We prove the completeness of both cones w.r.t. the energy-constrained diamond norm induced by $G$ (as an energy observable) and the coincidence of the second cone with the completion of the cone of CP linear maps w.r.t. this norm.\n  We show that the sets of quantum channels and quantum operations are complete w.r.t. the energy-constrained diamond "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10922","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1810.10922/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"}