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Parametric models and information geometry on W*-algebras

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arxiv 2207.09396 v1 pith:WVRJCDYT submitted 2022-07-19 math-ph math.MPquant-ph

Parametric models and information geometry on W*-algebras

classification math-ph math.MPquant-ph
keywords metrictensormodelsparametricalgebrasgeometryinformationriemannian
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We introduce the notion of smooth parametric model of normal positive linear functionals on possibly infinite-dimensional W*-algebras generalizing the notions of parametric models used in classical and quantum information geometry. We then use the Jordan product naturally available in this context in order to define a Riemannian metric tensor on parametric models satsfying suitable regularity conditions. This Riemannian metric tensor reduces to the Fisher-Rao metric tensor, or to the Fubini-Study metric tensor, or to the Bures-Helstrom metric tensor when suitable choices for the W*-algebra and the models are made.

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  1. Metric tensors and two-forms in information geometry from the GNS construction

    math-ph 2026-07 conditional novelty 7.0

    The real and imaginary parts of the dual GNS Hermitian product, pulled back by a canonical lift, yield the Fisher–Rao, Fubini–Study, and SLD geometries plus a two-form whose closedness is governed by the covariant der...