Related papers: Information geometry and local asymptotic normalit…
Geometrization of dynamics using (non)-affine parametization of arc length with time is investigated. The two archetypes of such parametrizations, the Eisenhart and the Jacobi metrics, are applied to a system of linear harmonic oscillators.…
There is a long history in both general relativity and quantum mechanics of removing fixed background structures, thereby making observed objects and measurement processes dynamical. We continue this evolution by combining central insights…
We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space…
We introduce a geometric formulation of quantum indeterminacy from which the standard uncertainty inequalities emerge as necessary consequences. Our approach is based on convex geometry in phase space and on methods from symplectic…
The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary…
Stationary quantum information sources emit sequences of correlated qudits -- that is, structured quantum stochastic processes. If an observer performs identical measurements on a qudit sequence, the outcomes are a realization of a…
This thesis explores important concepts in the area of quantum information geometry and their relationships. We highlight the unique characteristics of these concepts that arise from their quantum mechanical foundations and emphasize the…
This work presents a complete geometrical characterisation of divisible and indivisible time-evolution at the level of probabilities for systems with two configurations, open or closed. Our new geometrical construction in the space of…
The number of times that we can access a system to extract information via quantum metrology is always finite, and possibly small, and realistic amounts of prior knowledge tend to be moderate. Thus theoretical consistency demands a…
In this paper we study two entropic dynamical models from the viewpoint of information geometry. We study the geometry structures of the associated statistical manifolds. In order to analyse the character of the instability of the systems,…
A dynamical symmetry is employed to determine the structure of the quantum non-Markovian time-local master equation. Such a structure is composed from two components: scalar kinetic coefficients and the standard quantum Markovian operator…
We construct a canonical quantization of the two dimensional theory of a parametrized scalar field on noncompact spatial slices. The kinematics is built upon generalized charge-network states which are labelled by smooth embedding…
A central challenge in analog quantum simulation is to characterize desirable physical properties of quantum states produced in experiments. However, in conventional approaches, the extraction of arbitrary information requires performing…
Recent works have shown that generic local Hamiltonians can be efficiently inferred from local measurements performed on their eigenstates or thermal states. Realistic quantum systems are often affected by dissipation and decoherence due to…
Geometrical methods in quantum information are very promising for both providing technical tools and intuition into difficult control or optimization problems. Moreover, they are of fundamental importance in connecting pure geometrical…
The discovery of physical laws consistent with empirical observations lies at the heart of (applied) science and engineering. These laws typically take the form of nonlinear differential equations depending on parameters, dynamical systems…
We present a novel geometric approach for determining the unique structure of a Hamiltonian and establishing an instability criterion for quantum quadratic systems. Our geometric criterion provides insights into the underlying geometric…
Quantum information quantities, such as mutual information and entropies, are essential for characterizing quantum systems and protocols in quantum information science. In this contribution, we identify types of information measures based…
Information-theoretic quantities have received significant attention as system-independent measures of correlations in many-body quantum systems, e.g., as universal order parameters of synchronization. In this work, we present a method to…
We study an intermittent quasistatic dynamical system composed of nonuniformly hyperbolic Pomeau--Manneville maps with time-dependent parameters. We prove an ergodic theorem which shows almost sure convergence of time averages in a certain…