54 citations · 522 across the 59 of their papers we have counts for
19 papers · 1 filter
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…
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…
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…
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…
Group actions and monotone metric tensors: The qubit case
Florio M. Ciaglia, Fabio Di Nocera
In recent works, a link between group actions and information metrics on the space of faithful quantum states has been highlighted in particular cases. In this contribution, we giv…
Schwinger's picture of quantum mechanics: 2-groupoids and symmetries
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +2
Starting from the groupoid approach to Schwinger's picture of Quantum Mechanics, a proposal for the description of symmetries in this framework is advanced.It is shown that, given…
Schrödinger's problem with cats: measurements and states in the Groupoid Picture of Quantum Mechanics
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +1
Schrödinger's famous Gedankenexperiment involving a cat is used as a motivation to discuss the evolution of states of the composition of classical and quantum systems in the groupo…
Lagrangian description of Heisenberg and Landau-von Neumann equations of motion
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +3
An explicit Lagrangian description is given for the Heisenberg equation on the algebra of operators of a quantum system, and for the Landau-von Neumann equation on the manifold of…
Schwinger's Picture of Quantum Mechanics IV: Composition and independence
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +1
The groupoids description of Schwinger's picture of quantum mechanics is continued by discussing the closely related notions of composition of systems, subsystems, and their indepe…
Geometry from divergence functions and complex structures
Florio M. Ciaglia, Fabio Di Cosmo, Armando Figueroa +2
Motivated by the geometrical structures of quantum mechanics, we introduce an almost-complex structure on the product of any parallelizable statistical manifold …
Nonlinear Dynamics from Linear Quantum Evolutions
Florio M. Ciaglia, Fabio Di Cosmo, Armando Figueroa +5
Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be…
On the notion of composite system
Florio M. Ciaglia, Alberto Ibort, Giuseppe Marmo
The notion of composite system made up of distinguishable parties is investigated in the context of arbitrary convex spaces.
Stratified Manifold of Quantum States, actions of the complex special linear group
Dariusz Chruscinski, Florio M. Ciaglia, Alberto Ibort +2
We review the geometry of the space of quantum states of a finite-level quantum system with Hilbert space from a group-theoretical point of…
A gentle introduction to Schwinger's formulation of quantum mechanics: The groupoid picture
Florio M. Ciaglia, Alberto Ibort, Giuseppe Marmo
In this short letter we review Schwinger's formulation of Quantum Mechanics and we argue that the mathematical structure behind Schwinger's "Symbolism of Atomic Measurements" is th…
A Pedagogical Intrinsic Approach to Relative Entropies as Potential Functions of Quantum Metrics: the - Family
Florio M. Ciaglia, Fabio Di Cosmo, Marco Laudato +4
The so-called -z-\textit{Rényi Relative Entropies} provide a huge two-parameter family of relative entropies which includes almost all well-known examples of quantum relative en…
Dynamical aspects in the Quantizer-Dequantizer formalism
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +1
The use of the quantizer-dequantizer formalism to describe the evolution of a quantum system is reconsidered. We show that it is possible to embed a manifold in the space of quantu…
Dynamical Vector Fields on the Manifold of Quantum States
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +2
In this paper we shall consider the stratified manifold of quantum states and the vector fields which act on it. In particular, we show that the infinitesimal generator of the GKLS…
Time, classical and quantum
Paolo Aniello, Florio Maria Ciaglia, Fabio Di Cosmo +2
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator with a suitable real-valued f…