On the Lattice Structure of Probability Spaces in Quantum Mechanics

Let C be the set of all possible quantum states. We study the convex subsets of C with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes' M...

Descripción completa

Detalles Bibliográficos
Autores principales:	Holik, F., Massri, C., Plastino, A., Zuberman, L.
Formato:	JOUR
Materias:	Convex sets Entanglement MaxEnt approach Quantum information
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00207748_v52_n6_p1836_Holik
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_00207748_v52_n6_p1836_Holik
record_format	dspace
spelling	todo:paper_00207748_v52_n6_p1836_Holik2023-10-03T14:20:34Z On the Lattice Structure of Probability Spaces in Quantum Mechanics Holik, F. Massri, C. Plastino, A. Zuberman, L. Convex sets Entanglement MaxEnt approach Quantum information Let C be the set of all possible quantum states. We study the convex subsets of C with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes' Max-Ent principle. We also encounter links with entanglement witnesses, which leads to a new separability criteria expressed in lattice language. We also provide an extension of a separability criteria based on convex polytopes to the infinite dimensional case and show that it reveals interesting facets concerning the geometrical structure of the convex subsets. It is seen that the above mentioned framework is also capable of generalization to any statistical theory via the so-called convex operational models' approach. In particular, we show how to extend the geometrical structure underlying entanglement to any statistical model, an extension which may be useful for studying correlations in different generalizations of quantum mechanics. © 2012 Springer Science+Business Media, LLC. Fil:Holik, F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Massri, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Zuberman, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00207748_v52_n6_p1836_Holik
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Convex sets Entanglement MaxEnt approach Quantum information
spellingShingle	Convex sets Entanglement MaxEnt approach Quantum information Holik, F. Massri, C. Plastino, A. Zuberman, L. On the Lattice Structure of Probability Spaces in Quantum Mechanics
topic_facet	Convex sets Entanglement MaxEnt approach Quantum information
description	Let C be the set of all possible quantum states. We study the convex subsets of C with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes' Max-Ent principle. We also encounter links with entanglement witnesses, which leads to a new separability criteria expressed in lattice language. We also provide an extension of a separability criteria based on convex polytopes to the infinite dimensional case and show that it reveals interesting facets concerning the geometrical structure of the convex subsets. It is seen that the above mentioned framework is also capable of generalization to any statistical theory via the so-called convex operational models' approach. In particular, we show how to extend the geometrical structure underlying entanglement to any statistical model, an extension which may be useful for studying correlations in different generalizations of quantum mechanics. © 2012 Springer Science+Business Media, LLC.
format	JOUR
author	Holik, F. Massri, C. Plastino, A. Zuberman, L.
author_facet	Holik, F. Massri, C. Plastino, A. Zuberman, L.
author_sort	Holik, F.
title	On the Lattice Structure of Probability Spaces in Quantum Mechanics
title_short	On the Lattice Structure of Probability Spaces in Quantum Mechanics
title_full	On the Lattice Structure of Probability Spaces in Quantum Mechanics
title_fullStr	On the Lattice Structure of Probability Spaces in Quantum Mechanics
title_full_unstemmed	On the Lattice Structure of Probability Spaces in Quantum Mechanics
title_sort	on the lattice structure of probability spaces in quantum mechanics
url	http://hdl.handle.net/20.500.12110/paper_00207748_v52_n6_p1836_Holik
work_keys_str_mv	AT holikf onthelatticestructureofprobabilityspacesinquantummechanics AT massric onthelatticestructureofprobabilityspacesinquantummechanics AT plastinoa onthelatticestructureofprobabilityspacesinquantummechanics AT zubermanl onthelatticestructureofprobabilityspacesinquantummechanics
_version_	1807319911130726400

On the Lattice Structure of Probability Spaces in Quantum Mechanics

Ejemplares similares