18 citations · 151 across the 35 of their papers we have counts for
36 papers · 1 filter
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…
The Geometry of the solution space of first order Hamiltonian field theories III: Palatini's formulation of General Relativity
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +3
We complete the program started in two companion papers of defining a Poisson bracket structure on the space of solutions of the equations of motion of first order Hamiltonian fiel…
Some remarks on the notion of transitions
Florio M. Ciaglia aand Fabio Di Cosmo
In this paper some reflections on the concept of transition are presented: groupoids are introduced as models for the construction of a ``generalized logic'' whose basic statements…
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…