{"paper":{"title":"Exchangeable stochastic processes and symmetric states in quantum probability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.PR","authors_text":"Francesco Fidaleo, Vito Crismale","submitted_at":"2013-10-06T09:53:36Z","abstract_excerpt":"We analyze general aspects of exchangeable quantum stochastic processes, as well as some concrete cases relevant for several applications to Quantum Physics and Probability. We establish that there is a one-to-one correspondence between quantum stochastic processes, either preserving or not the identity, and states on free product C*-algebras, unital or not unital respectively, where the exchangeable ones correspond precisely to the symmetric states. We also connect some algebraic properties of exchangeable processes, that is the fact that they satisfy the product state or the block-singleton "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1566","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"}