Parametric models and information geometry on W*-algebras

• URL: http://arxiv.org/abs/2207.09396v1
• Date: Tue, 19 Jul 2022 16:44:54 GMT
• Title: Parametric models and information geometry on W*-algebras
• Authors: Florio M. Ciaglia, Fabio Di Nocera, J\"urgen Jost, Lorenz Schwachh\"ofer
• Abstract summary: We introduce the notion of smooth parametric model of normal positive linear functionals on possibly infinite-dimensional W*-algebras. We then use the Jordan product naturally available in this context to define a metric tensor on parametric models satsfying suitable regularity conditions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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