  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.
