3 citations · 5 across the 4 of their papers we have counts for
5 papers
Metric tensors and two-forms in information geometry from the GNS construction
Marco Castrillón López, Florio M. Ciaglia, Laura González-Bravo +1
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…
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 a categorical analogue of statistical covar…
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…
On the categorical foundations of quantum information theory: Categories and the Cramer-Rao inequality
Florio M. Ciaglia, Fabio Di Cosmo, Laura González-Bravo +2
An extension of Cencov's categorical description of classical inference theory to the domain of quantum systems is presented. It provides a novel categorical foundation to the theo…
Can Čencov meet Petz?
Florio M. Ciaglia, Fabio Di Cosmo, Laura González-Bravo
We discuss how to exploit the recent formulation of classical and quantum information geometry in terms of normal states on -algebras to formulate a problem that unifies Cen…