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arXiv · 2207.09396

Parametric models and information geometry on W*-algebras

Florio M. Ciaglia·Fabio Di Nocera·Jürgen Jost·Lorenz Schwachhöfer
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Abstract

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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Florio M. Ciaglia, Fabio Di Nocera, Jürgen Jost, Lorenz Schwachhöfer. 2022-07-19. Parametric models and information geometry on W*-algebras. https://doi.org/10.1007/s41884-022-00094-6

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