{"paper":{"title":"On the noncommutative deformation of the operator graph corresponding to the Klein group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"quant-ph","authors_text":"G.G. Amosov, I.Yu. Zhdanovskiy","submitted_at":"2016-04-18T13:37:37Z","abstract_excerpt":"We study the noncommutative operator graph ${\\mathcal L}_{\\theta }$ depending on complex parameter $\\theta $ recently introduced by M.E. Shirokov to construct channels with positive quantum zero-error capacity having vanishing n-shot capacity. We define the noncommutative group $G$ and the algebra ${\\mathcal A}_{\\theta }$ which is a quotient of ${\\mathbb C}G$ with respect to the special algebraic relation depending on $\\theta $ such that the matrix representation $\\phi $ of ${\\mathcal A}_{\\theta }$ results in the algebra ${\\mathcal M}_{\\theta }$ generated by ${\\mathcal L}_{\\theta }$. In the ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05387","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"}