Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy

Autores
Bellomo, Guido; Bosyk, Gustavo Martin; Holik, Federico Hernán; Zozor, Steeve
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Based on the problem of quantum data compression in a lossless way, we present here an operational interpretation for the family of quantum Rényi entropies. In order to do this, we appeal to a very general quantum encoding scheme that satisfies a quantum version of the Kraft-McMillan inequality. Then, in the standard situation, where one is intended to minimize the usual average length of the quantum codewords, we recover the known results, namely that the von Neumann entropy of the source bounds the average length of the optimal codes. Otherwise, we show that by invoking an exponential average length, related to an exponential penalization over large codewords, the quantum Rényi entropies arise as the natural quantities relating the optimal encoding schemes with the source description, playing an analogous role to that of von Neumann entropy.
Fil: Bellomo, Guido. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación; 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: Holik, Federico Hernán. 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: Zozor, Steeve. Université Grenoble Alpes; Francia
Materia
Quantum Variable-Length Code
Quantum Kraft-Mcmillan Inequality
Optimal Quantum Code
Quantum Renyi Entropy
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/53976
Acceder
id CONICETDig_c53584086509ac2109b0d6f08d37e49e
oai_identifier_str oai:ri.conicet.gov.ar:11336/53976
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropyBellomo, GuidoBosyk, Gustavo MartinHolik, Federico HernánZozor, SteeveQuantum Variable-Length CodeQuantum Kraft-Mcmillan InequalityOptimal Quantum CodeQuantum Renyi Entropyhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Based on the problem of quantum data compression in a lossless way, we present here an operational interpretation for the family of quantum Rényi entropies. In order to do this, we appeal to a very general quantum encoding scheme that satisfies a quantum version of the Kraft-McMillan inequality. Then, in the standard situation, where one is intended to minimize the usual average length of the quantum codewords, we recover the known results, namely that the von Neumann entropy of the source bounds the average length of the optimal codes. Otherwise, we show that by invoking an exponential average length, related to an exponential penalization over large codewords, the quantum Rényi entropies arise as the natural quantities relating the optimal encoding schemes with the source description, playing an analogous role to that of von Neumann entropy.Fil: Bellomo, Guido. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación; 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: Holik, Federico Hernán. 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: Zozor, Steeve. Université Grenoble Alpes; FranciaNature Publishing Group2017-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/53976Bellomo, Guido; Bosyk, Gustavo Martin; Holik, Federico Hernán; Zozor, Steeve; Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy; Nature Publishing Group; Scientific Reports; 7; 1; 12-2017; 1-102045-2322CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1038/s41598-017-13350-yinfo:eu-repo/semantics/altIdentifier/url/https://www.nature.com/articles/s41598-017-13350-yinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:32:00Zoai:ri.conicet.gov.ar:11336/53976instacron: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 15:32:00.388CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy
title Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy
spellingShingle Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy
Bellomo, Guido
Quantum Variable-Length Code
Quantum Kraft-Mcmillan Inequality
Optimal Quantum Code
Quantum Renyi Entropy
title_short Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy
title_full Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy
title_fullStr Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy
title_full_unstemmed Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy
title_sort Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy
dc.creator.none.fl_str_mv Bellomo, Guido
Bosyk, Gustavo Martin
Holik, Federico Hernán
Zozor, Steeve
author Bellomo, Guido
author_facet Bellomo, Guido
Bosyk, Gustavo Martin
Holik, Federico Hernán
Zozor, Steeve
author_role author
author2 Bosyk, Gustavo Martin
Holik, Federico Hernán
Zozor, Steeve
author2_role author
author
author
dc.subject.none.fl_str_mv Quantum Variable-Length Code
Quantum Kraft-Mcmillan Inequality
Optimal Quantum Code
Quantum Renyi Entropy
topic Quantum Variable-Length Code
Quantum Kraft-Mcmillan Inequality
Optimal Quantum Code
Quantum Renyi Entropy
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Based on the problem of quantum data compression in a lossless way, we present here an operational interpretation for the family of quantum Rényi entropies. In order to do this, we appeal to a very general quantum encoding scheme that satisfies a quantum version of the Kraft-McMillan inequality. Then, in the standard situation, where one is intended to minimize the usual average length of the quantum codewords, we recover the known results, namely that the von Neumann entropy of the source bounds the average length of the optimal codes. Otherwise, we show that by invoking an exponential average length, related to an exponential penalization over large codewords, the quantum Rényi entropies arise as the natural quantities relating the optimal encoding schemes with the source description, playing an analogous role to that of von Neumann entropy.
Fil: Bellomo, Guido. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación; 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: Holik, Federico Hernán. 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: Zozor, Steeve. Université Grenoble Alpes; Francia
description Based on the problem of quantum data compression in a lossless way, we present here an operational interpretation for the family of quantum Rényi entropies. In order to do this, we appeal to a very general quantum encoding scheme that satisfies a quantum version of the Kraft-McMillan inequality. Then, in the standard situation, where one is intended to minimize the usual average length of the quantum codewords, we recover the known results, namely that the von Neumann entropy of the source bounds the average length of the optimal codes. Otherwise, we show that by invoking an exponential average length, related to an exponential penalization over large codewords, the quantum Rényi entropies arise as the natural quantities relating the optimal encoding schemes with the source description, playing an analogous role to that of von Neumann entropy.
publishDate 2017
dc.date.none.fl_str_mv 2017-12
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/11336/53976
Bellomo, Guido; Bosyk, Gustavo Martin; Holik, Federico Hernán; Zozor, Steeve; Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy; Nature Publishing Group; Scientific Reports; 7; 1; 12-2017; 1-10
2045-2322
CONICET Digital
CONICET
url http://hdl.handle.net/11336/53976
identifier_str_mv Bellomo, Guido; Bosyk, Gustavo Martin; Holik, Federico Hernán; Zozor, Steeve; Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy; Nature Publishing Group; Scientific Reports; 7; 1; 12-2017; 1-10
2045-2322
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1038/s41598-017-13350-y
info:eu-repo/semantics/altIdentifier/url/https://www.nature.com/articles/s41598-017-13350-y
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Nature Publishing Group
publisher.none.fl_str_mv Nature Publishing Group
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
_version_ 1846083454456823808
score 13.22299

Publicaciones similares