{"paper":{"title":"On pure quasi quantum quadratic operators of M_2(C)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","quant-ph"],"primary_cat":"math.DS","authors_text":"Abduaziz Abduganiev, Farrukh Mukhamedov","submitted_at":"2013-06-11T02:00:32Z","abstract_excerpt":"In the present paper we study quasi quantum quadratic operators (q.q.o) acting on the algebra of $2\\times 2$ matrices $M_2(C)$. It is known that a channel is called pure if it sends pure states to pure ones. In this papers, we introduce a weaker condition, called $q$-purity, than purity of the channel. To study $q$-pure channels, we concentrate ourselves to quasi q.q.o. acting on $M_2(C)$. We describe all trace-preserving quasi q.q.o. on $M_2(C)$, which allowed us to prove that if a trace-preserving symmetric quasi q.q.o. such that the corresponding quadratic operator is linear, then its $q$-p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2403","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"}