{"paper":{"title":"Non-closure of quantum correlation matrices and factorizable channels that require infinite dimensional ancilla","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.OA","authors_text":"Magdalena Musat, Mikael R{\\o}rdam","submitted_at":"2018-06-26T23:11:37Z","abstract_excerpt":"We show that there exist factorizable quantum channels in each dimension $\\ge 11$ which do not admit a factorization through any finite dimensional von Neumann algebra, and do require ancillas of type II$_1$, thus witnessing new infinite-dimensional phenomena in quantum information theory. We show that the set of n by n matrices of correlations arising as second-order moments of projections in finite dimensional von Neumann algebras with a distinguished trace is non-closed, for all $n \\ge 5$, and we use this to give a simplified proof of the recent result of Dykema, Paulsen and Prakash that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10242","kind":"arxiv","version":4},"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"}