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...
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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 |
_version_ |
1768544440418304000 |