A quantum logical and geometrical approach to the study of improper mixtures

Autores
Domenech, Graciela; Holik, Federico Hernan; Massri, Cesar Dario
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study improper mixtures from a quantum logical and geometrical point of view. Taking into account the fact that improper mixtures do not admit an ignorance interpretation and must be considered as states in their own right, we do not follow the standard approach which considers improper mixtures as measures over the algebra of projections. Instead of it, we use the convex set of states in order to construct a new lattice whose atoms are all physical states: pure states and improper mixtures. This is done in order to overcome one of the problems which appear in the standard quantum logical formalism, namely, that for a subsystem of a larger system in an entangled state, the conjunction of all actual properties of the subsystem does not yield its actual state. In fact, its state is an improper mixture and cannot be represented in the von Neumann lattice as a minimal property which determines all other properties as is the case for pure states or classical systems. The new lattice also contains all propositions of the von Neumann lattice. We argue that this extension expresses in an algebraic form the fact that—alike the classical case—quantum interactions produce nontrivial correlations between the systems. Finally, we study the maps which can be defined between the extended lattice of a compound system and the lattices of its subsystems.
Fil: Domenech, Graciela. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomia y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomia y Física del Espacio; Argentina
Fil: Holik, Federico Hernan. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomia y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomia y Física del Espacio; Argentina
Fil: Massri, Cesar Dario. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Quantum Logic
Lattice theory
Improper Mixture
Propositional Algebra
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/16394
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A quantum logical and geometrical approach to the study of improper mixturesDomenech, GracielaHolik, Federico HernanMassri, Cesar DarioQuantum LogicLattice theoryImproper MixturePropositional Algebrahttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We study improper mixtures from a quantum logical and geometrical point of view. Taking into account the fact that improper mixtures do not admit an ignorance interpretation and must be considered as states in their own right, we do not follow the standard approach which considers improper mixtures as measures over the algebra of projections. Instead of it, we use the convex set of states in order to construct a new lattice whose atoms are all physical states: pure states and improper mixtures. This is done in order to overcome one of the problems which appear in the standard quantum logical formalism, namely, that for a subsystem of a larger system in an entangled state, the conjunction of all actual properties of the subsystem does not yield its actual state. In fact, its state is an improper mixture and cannot be represented in the von Neumann lattice as a minimal property which determines all other properties as is the case for pure states or classical systems. The new lattice also contains all propositions of the von Neumann lattice. We argue that this extension expresses in an algebraic form the fact that—alike the classical case—quantum interactions produce nontrivial correlations between the systems. Finally, we study the maps which can be defined between the extended lattice of a compound system and the lattices of its subsystems.Fil: Domenech, Graciela. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomia y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomia y Física del Espacio; ArgentinaFil: Holik, Federico Hernan. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomia y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomia y Física del Espacio; ArgentinaFil: Massri, Cesar Dario. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAmerican Institute Of Physics2010-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/16394Domenech, Graciela; Holik, Federico Hernan; Massri, Cesar Dario; A quantum logical and geometrical approach to the study of improper mixtures; American Institute Of Physics; Journal Of Mathematical Physics; 51; 5; 5-2010; 1-17; 0521080022-2488enginfo:eu-repo/semantics/altIdentifier/doi/10.1063/1.3429619info:eu-repo/semantics/altIdentifier/url/http://aip.scitation.org/doi/10.1063/1.3429619info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/0904.3472info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:51:22Zoai:ri.conicet.gov.ar:11336/16394instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:51:22.465CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A quantum logical and geometrical approach to the study of improper mixtures
title A quantum logical and geometrical approach to the study of improper mixtures
spellingShingle A quantum logical and geometrical approach to the study of improper mixtures
Domenech, Graciela
Quantum Logic
Lattice theory
Improper Mixture
Propositional Algebra
title_short A quantum logical and geometrical approach to the study of improper mixtures
title_full A quantum logical and geometrical approach to the study of improper mixtures
title_fullStr A quantum logical and geometrical approach to the study of improper mixtures
title_full_unstemmed A quantum logical and geometrical approach to the study of improper mixtures
title_sort A quantum logical and geometrical approach to the study of improper mixtures
dc.creator.none.fl_str_mv Domenech, Graciela
Holik, Federico Hernan
Massri, Cesar Dario
author Domenech, Graciela
author_facet Domenech, Graciela
Holik, Federico Hernan
Massri, Cesar Dario
author_role author
author2 Holik, Federico Hernan
Massri, Cesar Dario
author2_role author
author
dc.subject.none.fl_str_mv Quantum Logic
Lattice theory
Improper Mixture
Propositional Algebra
topic Quantum Logic
Lattice theory
Improper Mixture
Propositional Algebra
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study improper mixtures from a quantum logical and geometrical point of view. Taking into account the fact that improper mixtures do not admit an ignorance interpretation and must be considered as states in their own right, we do not follow the standard approach which considers improper mixtures as measures over the algebra of projections. Instead of it, we use the convex set of states in order to construct a new lattice whose atoms are all physical states: pure states and improper mixtures. This is done in order to overcome one of the problems which appear in the standard quantum logical formalism, namely, that for a subsystem of a larger system in an entangled state, the conjunction of all actual properties of the subsystem does not yield its actual state. In fact, its state is an improper mixture and cannot be represented in the von Neumann lattice as a minimal property which determines all other properties as is the case for pure states or classical systems. The new lattice also contains all propositions of the von Neumann lattice. We argue that this extension expresses in an algebraic form the fact that—alike the classical case—quantum interactions produce nontrivial correlations between the systems. Finally, we study the maps which can be defined between the extended lattice of a compound system and the lattices of its subsystems.
Fil: Domenech, Graciela. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomia y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomia y Física del Espacio; Argentina
Fil: Holik, Federico Hernan. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomia y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomia y Física del Espacio; Argentina
Fil: Massri, Cesar Dario. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We study improper mixtures from a quantum logical and geometrical point of view. Taking into account the fact that improper mixtures do not admit an ignorance interpretation and must be considered as states in their own right, we do not follow the standard approach which considers improper mixtures as measures over the algebra of projections. Instead of it, we use the convex set of states in order to construct a new lattice whose atoms are all physical states: pure states and improper mixtures. This is done in order to overcome one of the problems which appear in the standard quantum logical formalism, namely, that for a subsystem of a larger system in an entangled state, the conjunction of all actual properties of the subsystem does not yield its actual state. In fact, its state is an improper mixture and cannot be represented in the von Neumann lattice as a minimal property which determines all other properties as is the case for pure states or classical systems. The new lattice also contains all propositions of the von Neumann lattice. We argue that this extension expresses in an algebraic form the fact that—alike the classical case—quantum interactions produce nontrivial correlations between the systems. Finally, we study the maps which can be defined between the extended lattice of a compound system and the lattices of its subsystems.
publishDate 2010
dc.date.none.fl_str_mv 2010-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/16394
Domenech, Graciela; Holik, Federico Hernan; Massri, Cesar Dario; A quantum logical and geometrical approach to the study of improper mixtures; American Institute Of Physics; Journal Of Mathematical Physics; 51; 5; 5-2010; 1-17; 052108
0022-2488
url http://hdl.handle.net/11336/16394
identifier_str_mv Domenech, Graciela; Holik, Federico Hernan; Massri, Cesar Dario; A quantum logical and geometrical approach to the study of improper mixtures; American Institute Of Physics; Journal Of Mathematical Physics; 51; 5; 5-2010; 1-17; 052108
0022-2488
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1063/1.3429619
info:eu-repo/semantics/altIdentifier/url/http://aip.scitation.org/doi/10.1063/1.3429619
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/0904.3472
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Institute Of Physics
publisher.none.fl_str_mv American Institute Of Physics
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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