Information and Entanglement Measures in Quantum Systems With Applications to Atomic Physics

TL;DR

This thesis explores information, entanglement, and complexity in quantum systems, introducing new measures and criteria for entanglement and separability in various quantum contexts, with applications to atomic physics.

Contribution

It proposes new measures of spreading for orthogonal polynomials and introduces novel separability criteria for fermionic and continuous variable systems.

Findings

New separability criteria for pure states of N identical fermions

Analysis of entanglement in two-electron atoms

Introduction of measures of spreading for orthogonal polynomials

Abstract

This thesis is a multidisciplinary contribution to the information theory of single-particle Coulomb systems in their relativistic and not relativistic description, to the theory of special functions of mathematical physics with the proposal and analysis of a new set of measures of spreading for orthogonal polynomials, to quantum computation and learning devices and to the analysis of entanglement in systems of identical fermions, in this field we propose a separability criteria for pure states of N identical fermions and the entanglement of two-electron atoms is studied, a new separability criteria for continuous variable systems is also analyzed. The notions of information, complexity and entanglement play a central role.