54 citations · 522 across the 59 of their papers we have counts for
61 papers
A two-point approach to the inverse problem in information geometry
Florio M. Ciaglia, Giuseppe Marmo, Marco Pacelli +2
We formulate the inverse problem in information geometry within a two-point tensorial framework and solve it for general metric-affine manifolds, without imposing any curvature or…
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…
Potential functions in information geometry via bi-forms
Florio M. Ciaglia, Giuseppe Marmo, Marco Pacelli +2
In this paper we develop a general framework for potentials on Lauritzen manifolds, namely smooth manifolds equipped with a pseudo-Riemannian metric and a pair of conjugate affine…
Bi-forms Approach to Potential Functions in Information Geometry
Florio M. Ciaglia, Giuseppe Marmo, Marco Pacelli +2
Contrast functions play a fundamental role in information geometry, providing a means for generating the geometric structures of a statistical manifold: a pseudo-Riemannian metric…
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…
A coadjoint orbit-like construction for Jordan superalgebras
Florio M. Ciaglia, Shuhan Jiang, Jürgen Jost +1
We investigate the canonical pseudo-Riemannian metrics associated with Jordan-analogues of the coadjoint orbits for pseudo-Euclidean Jordan superalgebras.
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…
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…
Groupoid and algebra of the infinite quantum spin chain
Florio Maria Ciaglia, Fabio Di Cosmo, Paolo Facchi +3
It is well known that certain features of a quantum theory cannot be described in the standard picture on a Hilbert space. In particular, this happens when we try to formally frame…
The Geometry of the solution space of first order Hamiltonian field theories II: non-Abelian gauge theories
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +3
We go on with the program started in the companion paper [CDI+] of defining a Poisson bracket structure on the space of solutions of the equations of motion of first order Hamilton…
The Geometry of the solution space of first order Hamiltonian field theories I: from particle dynamics to free Electrodynamics
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +3
We analyse the problem of defining a Poisson bracket structure on the space of solutions of the equations of motions of first order Hamiltonian field theories. The cases of Hamilto…
Parametric models and information geometry on W*-algebras
Florio M. Ciaglia, Fabio Di Nocera, Jürgen Jost +1
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…
G-dual teleparallel connections in Information Geometry
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +1
Given a real, finite-dimensional, smooth parallelizable Riemannian manifold endowed with a teleparallel connection determined by a choice of a global bas…
Group actions and Monotone Quantum Metric Tensors
Florio M. Ciaglia, Fabio Di Nocera
The interplay between actions of Lie groups and monotone quantum metric tensors on the space of faithful quantum states of a finite-level system observed recently in DOI: 10.1140/e…
Dynamical maps and symmetroids
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +1
Starting from the canonical symmetroid associated with a groupoid , the issue of describing dynamical maps in the groupoidal approach to Quantum Mechanics is ad…
Quantum Tomography and Schwinger's Picture of Quantum Mechanics
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +1
In this paper the problem of tomographic reconstruction of states is investigated within the so-called Schwinger's picture of Quantum Mechanics in which a groupoid is associated wi…
Monotone metric tensors in Quantum Information Geometry
Florio M. Ciaglia, Fabio Di Cosmo, Fabio Di Nocera +1
We review some geometrical aspects pertaining to the world of monotone quantum metrics in finite dimensions. Particular emphasis is given to an unfolded perspective for quantum sta…
Information Geometry, Jordan Algebras, and a Coadjoint Orbit-Like Construction
Florio M. Ciaglia, Jürgen Jost, Lorenz Schwachhöfer
Jordan algebras arise naturally in (quantum) information geometry, and we want to understand their role and their structure within that framework. Inspired by Kirillov's discussion…
Symmetries and Covariant Poisson brackets on pre-symplectic manifolds
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +3
Noticing that the space of the solutions of a first order Hamiltonian field theory has a pre-symplectic structure, we describe a class of conserved charges on it associated to the…
Feynman's Propagator in Schwinger's picture of Quantum Mechanics
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +3
A novel derivation of Feynman's sum-over-histories construction of the quantum propagator using the groupoidal description of Schwinger picture of Quantum Mechanics is presented. I…
A quantum route to the classical Lagrangian formalism
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +3
Using the recently developed groupoidal description of Schwinger's picture of Quantum Mechanics, a new approach to Dirac's fundamental question on the role of the Lagrangian in Qua…