On the Lattice Structure of Probability Spaces in Quantum Mechanics

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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...

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Autores principales: Holik, Federico Hernán, Massri, César, Zuberman, Leandro
Publicado: 2013
Materias:
Convex sets
Entanglement
MaxEnt approach
Quantum information
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207748_v52_n6_p1836_Holik
http://hdl.handle.net/20.500.12110/paper_00207748_v52_n6_p1836_Holik
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00207748_v52_n6_p1836_Holik
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spelling paper:paper_00207748_v52_n6_p1836_Holik2023-06-08T14:41:59Z On the Lattice Structure of Probability Spaces in Quantum Mechanics Holik, Federico Hernán Massri, César Zuberman, Leandro 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. 2013 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207748_v52_n6_p1836_Holik 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, Federico Hernán
Massri, César
Zuberman, Leandro
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.
author Holik, Federico Hernán
Massri, César
Zuberman, Leandro
author_facet Holik, Federico Hernán
Massri, César
Zuberman, Leandro
author_sort Holik, Federico Hernán
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
publishDate 2013
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207748_v52_n6_p1836_Holik
http://hdl.handle.net/20.500.12110/paper_00207748_v52_n6_p1836_Holik
work_keys_str_mv AT holikfedericohernan onthelatticestructureofprobabilityspacesinquantummechanics
AT massricesar onthelatticestructureofprobabilityspacesinquantummechanics
AT zubermanleandro onthelatticestructureofprobabilityspacesinquantummechanics
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