{"paper":{"title":"Lyapunov exponents for Quantum Channels: an entropy formula and generic properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR","quant-ph"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes, Jader E. Brasil, Josue Knorst","submitted_at":"2019-08-22T23:14:50Z","abstract_excerpt":"We denote by $M_k$ the set of $k$ by $k$ matrices with complex entries. We consider quantum channels $\\phi_L$ of the form: given a measurable function $L:M_k\\to M_k$ and a measure $\\mu$ on $M_k$ we define the linear operator $\\phi_L:M_k \\to M_k$, by the law $\\rho \\,\\to\\,\\phi_L(\\rho) = \\int_{M_k} L(v) \\rho L(v)^\\dagger \\, \\dm(v).$\n  On a previous work the authors show that for a fixed measure $\\mu$ it is generic on the function $L$ the $\\Phi$-Erg property (also irreducibility). Here we will show that the purification property is also generic on $L$ for a fixed $\\mu$.\n  Given $L$ and $\\mu$ there"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08942","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/1908.08942/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"}