Quantum Entanglement: a Study of Recent Separability Criteria
Hansenne, Kiara
Promoteur(s) :
Bastin, Thierry
Date de soutenance : 29-jui-2020/30-jui-2020 • URL permanente : http://hdl.handle.net/2268.2/9319
Détails
Titre : | Quantum Entanglement: a Study of Recent Separability Criteria |
Titre traduit : | [fr] Intrication Quantique: une Étude de Critères de Séparabilité Récents |
Auteur : | Hansenne, Kiara ![]() |
Date de soutenance : | 29-jui-2020/30-jui-2020 |
Promoteur(s) : | Bastin, Thierry ![]() |
Membre(s) du jury : | Lumay, Geoffroy ![]() Martin, John ![]() Mathonet, Pierre ![]() Silhanek, Alejandro ![]() |
Langue : | Anglais |
Nombre de pages : | 75 |
Mots-clés : | [en] Quantum entanglement [en] Separability problem [en] Separability criteria [en] Bloch representation [fr] Intrication quantique [fr] Problème de séparabilité [fr] Critères de séparabilité [fr] Représentation de Bloch |
Discipline(s) : | Physique, chimie, mathématiques & sciences de la terre > Physique |
Public cible : | Chercheurs Professionnels du domaine Etudiants |
Institution(s) : | Université de Liège, Liège, Belgique |
Diplôme : | Master en sciences physiques, à finalité approfondie |
Faculté : | Mémoires de la Faculté des Sciences |
Résumé
[en] The theory of quantum entanglement is still under construction and has generated great interest over the last thirty years. Indeed, determining whether a given quantum state is entangled or not is still an open problem today in physics, known as the separability problem. In this manuscript, we aim at giving a selective but up to date review of the separability problem. We focus on the theoretical perspective of the problem. Theoretically, quantum entanglement is defined by a mathematical property of quantum states that are described by density operators acting on Hilbert spaces. We first explicit this definition and introduce some basis notions of the entanglement theory such as the Bloch representation of quantum states. Then, we present and analyse several separability criteria. We begin with the most important ones developed from 1996 to 2003, that is the PPT criterion, criteria based on entanglement witnesses, on entanglement measures (such as negativity or concurrences) and the CCNR criterion. We then move on to more recent criteria, developed from 2009 to 2020. Most of them make use of the Bloch representation. We finally conclude by comparing the exposed criteria.
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