{"paper":{"title":"Diagonalizability of non homogeneous quantum Markov states and associated von Neumann algebras","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.OA","authors_text":"Farruh Mukhamedov, Francesco Fidaleo","submitted_at":"2004-11-09T16:19:15Z","abstract_excerpt":"We clarify the meaning of diagonalizability of quantum Markov states. Then, we prove that each non homogeneous quantum Markov state is diagonalizable. Namely, for each Markov state $\\phi$ on the spin algebra $A:={\\bar{\\otimes_{j\\in Z}M_{d_{j}}}^{C^{*}}}$ there exists a suitable maximal Abelian subalgebra $D\\subset A$, a Umegaki conditional expectation $E:A\\mapsto D$ and a Markov measure $\\mu$ on $spec(D)$ such that $\\phi=\\phi_{\\mu}\\circ E$, the Markov state $\\phi_{\\mu}$, being the state on $D$ arising from the measure $\\mu$. An analogous result is true for non homogeneous quantum processes bas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411200","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0411200/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"}