{"paper":{"title":"On the structure of positive maps; finite dimensional case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Wladyslaw A. Majewski","submitted_at":"2010-05-21T13:04:30Z","abstract_excerpt":"A natural and intrinsic characterization of the structure of the set $\\mathfrak{C}$ of positive unital maps is given, i.e. it is shown that $\\mathfrak{C}$ is isometrically isomorphic to the subset $\\gD$ of bp-positive density matrices endowed with the geometry given by the norm $\\alpha$ dual to the Grothendieck projective norm $\\pi$, the structure of $\\gD$ is determined by the set of its exposed points, and finally a characterization of exposed points of $\\gD$ in terms of convex analysis is presented. This seems to be an answer to an old open problem, characterization of the structure of the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.3949","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"}