3 papers
math-ph2026
Metric tensors and two-forms in information geometry from the GNS construction
Marco Castrillón López, M. Castrillón López, F. M. Ciaglia +5
We develop a GNS-based construction of geometric tensors on smooth parametric statistical models over -algebras. Since the state space of a -algebra is generally not a sm…
math-ph2025
Fields of covariances on non-commutative probability spaces in finite dimensions
Florio M. Ciaglia, Fabio Di Cosmo, Laura González-Bravo
We introduce the notion of a field of covariances, a contravariant functor from non-commutative probability spaces to Hilbert spaces, as the natural categorical analogue of statist…
math-ph2025
Towards a category-theoretic foundation of Classical and Quantum Information Geometry
Florio M. Ciaglia, Fabio Di Cosmo, Laura González-Bravo
We introduce the category , whose objects are pairs of W-algebras and normal states and whose morphisms are state-preserving unital completely positive (CPU) m…