{"paper":{"title":"A Sufficient Criterion for Divisibility of Quantum Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Frederik vom Ende","submitted_at":"2024-07-24T08:58:02Z","abstract_excerpt":"We present a simple, dimension-independent criterion which guarantees that some quantum channel $\\Phi$ is divisible, i.e. that there exists a non-trivial factorization $\\Phi=\\Phi_1\\Phi_2$. The idea is to first define an \"elementary\" channel $\\Phi_2$ and then to analyze when $\\Phi\\Phi_2^{-1}$ is completely positive. The sufficient criterion obtained this way -- which even yields an explicit factorization of $\\Phi$ -- is that one has to find orthogonal unit vectors $x,x^\\perp$ such that $\\langle x^\\perp|\\mathcal K_\\Phi\\mathcal K_\\Phi^\\perp|x\\rangle=\\langle x|\\mathcal K_\\Phi\\mathcal K_\\Phi^\\perp|"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.17103","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.17103/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"}