Beyond Landau-Pollak and entropic inequalities: Geometric bounds imposed on uncertainties sums

Autores
Zozor, Steeve; Bosyk, Gustavo Martin; Portesi, Mariela Adelina; Osán, Tristán Martín; Lamberti, Pedro Walter
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we propose generalized inequalities to quantify the uncertainty principle. We deal with two observables with finite discrete spectra described by positive operator-valued measures (POVM) and with systems in mixed states. Denoting by p(A;ρ) and p(B;ρ) the probability vectors associated with observables A and B when the system is in the state ρ, we focus on relations of the form U_α(p(A;ρ))+U_β (p(B;ρ)) ≥ B_{α,β} (A,B) where U_λ is a measure of uncertainty and B is a non-trivial state-independent bound for the uncertainty sum. We propose here: (i) an extension of the usual Landau?Pollak inequality for uncertainty measures of the form U_f (p(A;ρ)) = f(max_i p_i(A;ρ)) issued from well suited metrics; our generalization comes out as a consequence of the triangle inequality. The original Landau?Pollak inequality initially proved for nondegenerate observables and pure states, appears to be the most restrictive one in terms of the maximal probabilities; (ii) an entropic formulation for which the uncertainty measure is based on generalized entropies of Rényi or Havrda?Charvát?Tsallis type: U_{g,α}(p(A;ρ)) = g(Σ_i[p_i(A;ρ)]^α)/(1−α). Our approach is based on Schur-concavity considerations and on previously derived Landau?Pollak type inequalities.
Fil: Zozor, Steeve. Université Grenoble Alpes; Francia. Grenoble Images Parole Signal Automatique; Francia
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
Fil: Osán, Tristán Martín. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Materia
GENERALIZED UNCERTAINTY RELATIONS
LANDAU-POLLAK TYPE INEQUALITIES
ENTROPIC UNCERTAINTY RELATION
PURE AND MIXED STATES
POVM
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:11336/101955
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/101955
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Beyond Landau-Pollak and entropic inequalities: Geometric bounds imposed on uncertainties sumsZozor, SteeveBosyk, Gustavo MartinPortesi, Mariela AdelinaOsán, Tristán MartínLamberti, Pedro WalterGENERALIZED UNCERTAINTY RELATIONSLANDAU-POLLAK TYPE INEQUALITIESENTROPIC UNCERTAINTY RELATIONPURE AND MIXED STATESPOVMhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1In this paper we propose generalized inequalities to quantify the uncertainty principle. We deal with two observables with finite discrete spectra described by positive operator-valued measures (POVM) and with systems in mixed states. Denoting by p(A;ρ) and p(B;ρ) the probability vectors associated with observables A and B when the system is in the state ρ, we focus on relations of the form U_α(p(A;ρ))+U_β (p(B;ρ)) ≥ B_{α,β} (A,B) where U_λ is a measure of uncertainty and B is a non-trivial state-independent bound for the uncertainty sum. We propose here: (i) an extension of the usual Landau?Pollak inequality for uncertainty measures of the form U_f (p(A;ρ)) = f(max_i p_i(A;ρ)) issued from well suited metrics; our generalization comes out as a consequence of the triangle inequality. The original Landau?Pollak inequality initially proved for nondegenerate observables and pure states, appears to be the most restrictive one in terms of the maximal probabilities; (ii) an entropic formulation for which the uncertainty measure is based on generalized entropies of Rényi or Havrda?Charvát?Tsallis type: U_{g,α}(p(A;ρ)) = g(Σ_i[p_i(A;ρ)]^α)/(1−α). Our approach is based on Schur-concavity considerations and on previously derived Landau?Pollak type inequalities.Fil: Zozor, Steeve. Université Grenoble Alpes; Francia. Grenoble Images Parole Signal Automatique; FranciaFil: 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; ArgentinaFil: Osán, Tristán Martín. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaAmerican Physical Society2015-02-17info: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/11336/101955Zozor, Steeve; Bosyk, Gustavo Martin; Portesi, Mariela Adelina; Osán, Tristán Martín; Lamberti, Pedro Walter; Beyond Landau-Pollak and entropic inequalities: Geometric bounds imposed on uncertainties sums; American Physical Society; AIP Conference Proceedings; 1641; 1; 17-2-2015; 181-1880094-243X1551-7616CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4905977info:eu-repo/semantics/altIdentifier/doi/10.1063/1.4905977info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:15:52Zoai:ri.conicet.gov.ar:11336/101955instacron: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:34982025-09-10 13:15:52.283CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Beyond Landau-Pollak and entropic inequalities: Geometric bounds imposed on uncertainties sums
title Beyond Landau-Pollak and entropic inequalities: Geometric bounds imposed on uncertainties sums
spellingShingle Beyond Landau-Pollak and entropic inequalities: Geometric bounds imposed on uncertainties sums
Zozor, Steeve
GENERALIZED UNCERTAINTY RELATIONS
LANDAU-POLLAK TYPE INEQUALITIES
ENTROPIC UNCERTAINTY RELATION
PURE AND MIXED STATES
POVM
title_short Beyond Landau-Pollak and entropic inequalities: Geometric bounds imposed on uncertainties sums
title_full Beyond Landau-Pollak and entropic inequalities: Geometric bounds imposed on uncertainties sums
title_fullStr Beyond Landau-Pollak and entropic inequalities: Geometric bounds imposed on uncertainties sums
title_full_unstemmed Beyond Landau-Pollak and entropic inequalities: Geometric bounds imposed on uncertainties sums
title_sort Beyond Landau-Pollak and entropic inequalities: Geometric bounds imposed on uncertainties sums
dc.creator.none.fl_str_mv Zozor, Steeve
Bosyk, Gustavo Martin
Portesi, Mariela Adelina
Osán, Tristán Martín
Lamberti, Pedro Walter
author Zozor, Steeve
author_facet Zozor, Steeve
Bosyk, Gustavo Martin
Portesi, Mariela Adelina
Osán, Tristán Martín
Lamberti, Pedro Walter
author_role author
author2 Bosyk, Gustavo Martin
Portesi, Mariela Adelina
Osán, Tristán Martín
Lamberti, Pedro Walter
author2_role author
author
author
author
dc.subject.none.fl_str_mv GENERALIZED UNCERTAINTY RELATIONS
LANDAU-POLLAK TYPE INEQUALITIES
ENTROPIC UNCERTAINTY RELATION
PURE AND MIXED STATES
POVM
topic GENERALIZED UNCERTAINTY RELATIONS
LANDAU-POLLAK TYPE INEQUALITIES
ENTROPIC UNCERTAINTY RELATION
PURE AND MIXED STATES
POVM
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we propose generalized inequalities to quantify the uncertainty principle. We deal with two observables with finite discrete spectra described by positive operator-valued measures (POVM) and with systems in mixed states. Denoting by p(A;ρ) and p(B;ρ) the probability vectors associated with observables A and B when the system is in the state ρ, we focus on relations of the form U_α(p(A;ρ))+U_β (p(B;ρ)) ≥ B_{α,β} (A,B) where U_λ is a measure of uncertainty and B is a non-trivial state-independent bound for the uncertainty sum. We propose here: (i) an extension of the usual Landau?Pollak inequality for uncertainty measures of the form U_f (p(A;ρ)) = f(max_i p_i(A;ρ)) issued from well suited metrics; our generalization comes out as a consequence of the triangle inequality. The original Landau?Pollak inequality initially proved for nondegenerate observables and pure states, appears to be the most restrictive one in terms of the maximal probabilities; (ii) an entropic formulation for which the uncertainty measure is based on generalized entropies of Rényi or Havrda?Charvát?Tsallis type: U_{g,α}(p(A;ρ)) = g(Σ_i[p_i(A;ρ)]^α)/(1−α). Our approach is based on Schur-concavity considerations and on previously derived Landau?Pollak type inequalities.
Fil: Zozor, Steeve. Université Grenoble Alpes; Francia. Grenoble Images Parole Signal Automatique; Francia
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
Fil: Osán, Tristán Martín. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
description In this paper we propose generalized inequalities to quantify the uncertainty principle. We deal with two observables with finite discrete spectra described by positive operator-valued measures (POVM) and with systems in mixed states. Denoting by p(A;ρ) and p(B;ρ) the probability vectors associated with observables A and B when the system is in the state ρ, we focus on relations of the form U_α(p(A;ρ))+U_β (p(B;ρ)) ≥ B_{α,β} (A,B) where U_λ is a measure of uncertainty and B is a non-trivial state-independent bound for the uncertainty sum. We propose here: (i) an extension of the usual Landau?Pollak inequality for uncertainty measures of the form U_f (p(A;ρ)) = f(max_i p_i(A;ρ)) issued from well suited metrics; our generalization comes out as a consequence of the triangle inequality. The original Landau?Pollak inequality initially proved for nondegenerate observables and pure states, appears to be the most restrictive one in terms of the maximal probabilities; (ii) an entropic formulation for which the uncertainty measure is based on generalized entropies of Rényi or Havrda?Charvát?Tsallis type: U_{g,α}(p(A;ρ)) = g(Σ_i[p_i(A;ρ)]^α)/(1−α). Our approach is based on Schur-concavity considerations and on previously derived Landau?Pollak type inequalities.
publishDate 2015
dc.date.none.fl_str_mv 2015-02-17
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/11336/101955
Zozor, Steeve; Bosyk, Gustavo Martin; Portesi, Mariela Adelina; Osán, Tristán Martín; Lamberti, Pedro Walter; Beyond Landau-Pollak and entropic inequalities: Geometric bounds imposed on uncertainties sums; American Physical Society; AIP Conference Proceedings; 1641; 1; 17-2-2015; 181-188
0094-243X
1551-7616
CONICET Digital
CONICET
url http://hdl.handle.net/11336/101955
identifier_str_mv Zozor, Steeve; Bosyk, Gustavo Martin; Portesi, Mariela Adelina; Osán, Tristán Martín; Lamberti, Pedro Walter; Beyond Landau-Pollak and entropic inequalities: Geometric bounds imposed on uncertainties sums; American Physical Society; AIP Conference Proceedings; 1641; 1; 17-2-2015; 181-188
0094-243X
1551-7616
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://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4905977
info:eu-repo/semantics/altIdentifier/doi/10.1063/1.4905977
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 American Physical Society
publisher.none.fl_str_mv American Physical Society
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 12.993085

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