Aspects géométriques des corrélations quantiques dans des systèmes multiqudits.

Abstract

The quantum mechanics is a fundamental theory to describe the physical reality of the microscopic world. The geometric formulation of quantum mechanics aims at giving a unified description of physical systems based on its underlying geometric structures. This PhD thesis is entitled “Geometric aspects of quantum correlations in multiqudit systems”. It aims at studying the pure states space of a collection of qudits through two approaches: the first one aims at exploring the different geometric structures of the manifold associated to the space of pure states, namely, the Kähler form, the Fubini-Study metric, the curvature, the Berry-Simon connection, the geometric phase, etc. The second one aims at studying the dynamics of the system through the evaluation of the evolution speed and the geodesic distance which considerably simplify the solution of the quantum brachistochrone problem. These two approaches have been examined in relation with the quantum entanglement for the bipartite systems. The results examined and discussed in this work give a very interesting insight into the geometric structures of quantum systems and our understanding of the geometric nature of the quantum information theory.