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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/101872
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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 Técnicas2025-09-29T10:37:46Zoai: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:34982025-09-29 10:37:47.117CONICET 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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13.070432 |