Basics of Quantum Mechanics, Geometrization and some Applications to Quantum Information

Simple item page
dc.creatorClemente-Gallardo, J.
dc.creatorMarmo, G.
dc.date2008-06-28
dc.date.accessioned2026-07-07T13:02:15Z
dc.date.available2026-07-07T13:02:15Z
dc.descriptionIn this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schrödinger framework from this perspective and provide a description of the Weyl-Wigner construction. Finally, after reviewing the basics of the geometric formulation of quantum mechanics, we apply the methods presented to the most interesting cases of finite dimensional Hilbert spaces: those of two, three and four level systems (one qubit, one qutrit and two qubit systems). As a more practical application, we discuss the advantages that the geometric formulation of quantum mechanics can provide us with in the study of situations as the functional independence of entanglement witnesses.
dc.descriptionAmsLaTeX, 37 pages, 8 figures. This paper is an expanded version of some lectures delivered by one of us (G. M.) at the ``Advanced Winter School on the Mathematical Foundation of Quantum Control and Quantum Information'' which took place at Castro Urdiales (Spain), February 11-15, 2008
dc.identifierhttps://arxiv.org/abs/0806.4701
dc.identifierhttp://arxiv.org/abs/0806.4701
dc.identifierInt.J.Geom.Meth.Mod.Phys.5:989-1032,2008
dc.identifierdoi:10.1142/S0219887808003156
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/226390
dc.subjectQuantum Physics
dc.titleBasics of Quantum Mechanics, Geometrization and some Applications to Quantum Information
dc.typetext

Files

Collections

arXiv