{"paper":{"title":"On Bures-Distance and *-Algebraic Transition Probability between Inner Derived Positive Linear Forms over W*-Algebra","license":"","headline":"","cross_cats":["math.MP","math.OA"],"primary_cat":"math-ph","authors_text":"Armin Uhlmann, Peter M. Alberti","submitted_at":"2002-02-25T18:42:58Z","abstract_excerpt":"On a W*-algebra M, for given two positive linear forms f,g and algebra elements a,b a variational expression for the Bures-distance d_B(f^a,g^b) between the inner derived positive linear forms f^a=f(a* . a) and g^b=g(b* . b) is obtained. Along with the proof of the formula also some earlier result of S.Gudder on non-commutative probability will be slightly extended. Also, the given expression of the Bures-distance nicely relates to some system of seminorms proposed by D.Buchholz and which occured along with the problem of estimating the so-called `weak intertwiners' in algebraic quantum field "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0202038","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"}