Parametric models and information geometry on W*-algebras Articles uri icon

publication date

  • January 2023

start page

  • 329

end page

  • 354

volume

  • 7 (2024)

International Standard Serial Number (ISSN)

  • 2511-2481

Electronic International Standard Serial Number (EISSN)

  • 2511-249X

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.

subjects

  • Mathematics

keywords

  • probability distributions; quantum states; c *-algebras; banach manifolds