Related papers: Information geometry and local asymptotic normalit…
Imaging systems are represented as linear operators, and their singular value spectra describe the structure recoverable at the operator level. Building on an operator-based information-theoretic framework, this paper introduces a minimal…
Physical systems behave according to their underlying dynamical equations which, in turn, can be identified from experimental data. Explaining data requires selecting mathematical models that best capture the data regularities. Identifying…
Recent advancements have revealed new links between information geometry and classical stochastic thermodynamics, particularly through the Fisher information (FI) with respect to time. Recognizing the non-uniqueness of the quantum Fisher…
We study the open dynamics of a quantum two-level system coupled to an environment modeled by random matrices. Using the quantum channel formalism, we investigate different quantum Markovianity measures and criteria. A thorough analysis of…
In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…
We propose a unified theoretical framework for quantifying spatio-temporal interactions in a stochastic dynamical system based on information geometry. In the proposed framework, the degree of interactions is quantified by the divergence…
It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to the…
It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…
Information geometry and inductive inference methods can be used to model dynamical systems in terms of their probabilistic description on curved statistical manifolds. In this article, we present a formal conceptual reexamination of the…
Non-Markovian evolution in open quantum systems is often characterized in terms of the backflow of information from environment to system and is thus an important facet in investigating the performance and robustness of quantum information…
We propose a general formulation of the renormalisation group as a family of quantum channels which connect the microscopic physical world to the observable world at some scale. By endowing the set of quantum states with an operationally…
The dynamics of local observables in a quantum many-body system can be formally described in the language of open systems. The problem is that the bath representing the complement of the local subsystem generally does not allow the common…
This article elaborates on entanglement entropy and quantum information theory of geometric flows of (relativistic) Lagrange--Hamilton mechanical systems. A set of basic geometric and quantum mechanics and probability concepts together with…
We address the dynamics of quantum correlations in continuous variable open systems and analyze the evolution of bipartite Gaussian states in independent noisy channels. In particular, upon introducing the notion of dynamical path through a…
In this paper, I propose a theoretical information-geometric framework suitable to characterize chaotic dynamical behavior of arbitrary complex systems on curved statistical manifolds. Specifically, I present an information-geometric…
Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the…
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be…
Informational dependence between statistical or quantum subsystems can be described with Fisher matrix or Fubini-Study metric obtained from variations of the sample/configuration space coordinates. Using these non-covariant objects as…
We introduce a new tool for the quantitative characterisation of the departure form Markovianity of a given dynamical process. Our tool can be applied to a generic $N$-level system and extended straightforwardly to Gaussian…
The paper is the first of two parts of the work devoted to the investigation of constructing quantum theory of a closed universe as a system without asynptotic states. In Part I the role of asymptotic states in quantum theory of gravity is…