On a generalized entropic uncertainty relation in the case of the qubit

Autores
Zozor, Steeve; Bosyk, Gustavo Martin; Portesi, Mariela Adelina
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two-dimensional Hilbert space. Rényi entropy is used as an uncertainty measure associated with the distribution probabilities corresponding to the outcomes of the observables. We derive a general expression for the tight lower bound of the sum of Rényi entropies for any couple of (positive) entropic indices (alpha, beta). Thus, we have overcome the Hölder conjugacy constraint imposed on the entropic indices by Riesz-Thorin theorem. In addition, we present an analytical expression for the tight bound inside the square [0,1/2]x[0,1/2] in the alpha-beta plane, and a semi-analytical expression on the line beta=alpha. It is seen that previous results are included as particular cases. Moreover we present a semi-analytical, suboptimal bound for any couple of indices. In all cases, we provide the minimizing states.
Fil: Zozor, Steeve. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Bosyk, Gustavo Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Portesi, Mariela Adelina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Materia
ENTROPIC MEASURES
UNCERTAINTY RELATION
QUBIT SYSTEM
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:11336/101872
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/101872
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On a generalized entropic uncertainty relation in the case of the qubitZozor, SteeveBosyk, Gustavo MartinPortesi, Mariela AdelinaENTROPIC MEASURESUNCERTAINTY RELATIONQUBIT SYSTEMhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two-dimensional Hilbert space. Rényi entropy is used as an uncertainty measure associated with the distribution probabilities corresponding to the outcomes of the observables. We derive a general expression for the tight lower bound of the sum of Rényi entropies for any couple of (positive) entropic indices (alpha, beta). Thus, we have overcome the Hölder conjugacy constraint imposed on the entropic indices by Riesz-Thorin theorem. In addition, we present an analytical expression for the tight bound inside the square [0,1/2]x[0,1/2] in the alpha-beta plane, and a semi-analytical expression on the line beta=alpha. It is seen that previous results are included as particular cases. Moreover we present a semi-analytical, suboptimal bound for any couple of indices. In all cases, we provide the minimizing states.Fil: Zozor, Steeve. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Bosyk, Gustavo Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Portesi, Mariela Adelina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaIOP Publishing2013-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/101872Zozor, Steeve; Bosyk, Gustavo Martin; Portesi, Mariela Adelina; On a generalized entropic uncertainty relation in the case of the qubit; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 46; 46; 11-2013; 465301-4653171751-8113CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/1751-8121/46/46/465301/article?fromSearchPage=trueinfo:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/46/46/465301info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:35:10Zoai:ri.conicet.gov.ar:11336/101872instacron: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:34982025-10-15 15:35:10.462CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On a generalized entropic uncertainty relation in the case of the qubit
title On a generalized entropic uncertainty relation in the case of the qubit
spellingShingle On a generalized entropic uncertainty relation in the case of the qubit
Zozor, Steeve
ENTROPIC MEASURES
UNCERTAINTY RELATION
QUBIT SYSTEM
title_short On a generalized entropic uncertainty relation in the case of the qubit
title_full On a generalized entropic uncertainty relation in the case of the qubit
title_fullStr On a generalized entropic uncertainty relation in the case of the qubit
title_full_unstemmed On a generalized entropic uncertainty relation in the case of the qubit
title_sort On a generalized entropic uncertainty relation in the case of the qubit
dc.creator.none.fl_str_mv Zozor, Steeve
Bosyk, Gustavo Martin
Portesi, Mariela Adelina
author Zozor, Steeve
author_facet Zozor, Steeve
Bosyk, Gustavo Martin
Portesi, Mariela Adelina
author_role author
author2 Bosyk, Gustavo Martin
Portesi, Mariela Adelina
author2_role author
author
dc.subject.none.fl_str_mv ENTROPIC MEASURES
UNCERTAINTY RELATION
QUBIT SYSTEM
topic ENTROPIC MEASURES
UNCERTAINTY RELATION
QUBIT SYSTEM
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two-dimensional Hilbert space. Rényi entropy is used as an uncertainty measure associated with the distribution probabilities corresponding to the outcomes of the observables. We derive a general expression for the tight lower bound of the sum of Rényi entropies for any couple of (positive) entropic indices (alpha, beta). Thus, we have overcome the Hölder conjugacy constraint imposed on the entropic indices by Riesz-Thorin theorem. In addition, we present an analytical expression for the tight bound inside the square [0,1/2]x[0,1/2] in the alpha-beta plane, and a semi-analytical expression on the line beta=alpha. It is seen that previous results are included as particular cases. Moreover we present a semi-analytical, suboptimal bound for any couple of indices. In all cases, we provide the minimizing states.
Fil: Zozor, Steeve. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Bosyk, Gustavo Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Portesi, Mariela Adelina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
description We revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two-dimensional Hilbert space. Rényi entropy is used as an uncertainty measure associated with the distribution probabilities corresponding to the outcomes of the observables. We derive a general expression for the tight lower bound of the sum of Rényi entropies for any couple of (positive) entropic indices (alpha, beta). Thus, we have overcome the Hölder conjugacy constraint imposed on the entropic indices by Riesz-Thorin theorem. In addition, we present an analytical expression for the tight bound inside the square [0,1/2]x[0,1/2] in the alpha-beta plane, and a semi-analytical expression on the line beta=alpha. It is seen that previous results are included as particular cases. Moreover we present a semi-analytical, suboptimal bound for any couple of indices. In all cases, we provide the minimizing states.
publishDate 2013
dc.date.none.fl_str_mv 2013-11
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/11336/101872
Zozor, Steeve; Bosyk, Gustavo Martin; Portesi, Mariela Adelina; On a generalized entropic uncertainty relation in the case of the qubit; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 46; 46; 11-2013; 465301-465317
1751-8113
CONICET Digital
CONICET
url http://hdl.handle.net/11336/101872
identifier_str_mv Zozor, Steeve; Bosyk, Gustavo Martin; Portesi, Mariela Adelina; On a generalized entropic uncertainty relation in the case of the qubit; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 46; 46; 11-2013; 465301-465317
1751-8113
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/1751-8121/46/46/465301/article?fromSearchPage=true
info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/46/46/465301
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
application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
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 13.22299

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