{"paper":{"title":"On Faces of the set of Quantum Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"quant-ph","authors_text":"Raphael Loewy","submitted_at":"2016-09-18T09:30:04Z","abstract_excerpt":"A linear map $L$ from ${\\mathbb C}^{n \\times n}$ into ${\\mathbb C}^{n \\times n}$ is called a quantum channel if it is completely positive and trace preserving. The set ${\\cal L}_n$ of all such quantum channels is known to be a compact convex set. While the extreme points of ${\\cal L}_n$ can be characterized, not much is known about the structure of its higher dimensional faces. Using the so called Choi matrix $Z(L)$ associated with the quantum channel $L$, we compute the maximum dimension of a proper face of ${\\cal L}_n$, and in addition the possible dimensions of faces generated by $L$ when $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05890","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":""},"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"}