Generalized perfect codes for symmetric classical-quantum channels

We define a new family of codes for symmetric classical-quantum channels and establish their optimality. To this end, we extend the classical notion of generalized perfect and quasi-perfect codes to channels defined over some finite dimensional complex Hilbert output space. The resulting optimality...

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Detalles Bibliográficos
Autores: Blasco Coll, Andreu, Vázquez Vilar, Gonzalo, Rodríguez Fonollosa, Javier|||0000-0002-0136-2586
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/373658
Acceso en línea:https://hdl.handle.net/2117/373658
https://dx.doi.org/10.1109/TIT.2022.3170868
Access Level:acceso abierto
Palabra clave:Quantum communication
Error-correcting codes (Information theory)
Codes
Error probability
Quantum channels
Channel capacity
Quantum system
Task analysis
Quantum state
Comunicació quàntica
Codis correctors d'errors (Teoria de la informació)
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
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spelling Generalized perfect codes for symmetric classical-quantum channelsBlasco Coll, AndreuVázquez Vilar, GonzaloRodríguez Fonollosa, Javier|||0000-0002-0136-2586Quantum communicationError-correcting codes (Information theory)CodesError probabilityQuantum channelsChannel capacityQuantum systemTask analysisQuantum stateComunicació quànticaCodis correctors d'errors (Teoria de la informació)Àrees temàtiques de la UPC::Informàtica::Informàtica teòricaWe define a new family of codes for symmetric classical-quantum channels and establish their optimality. To this end, we extend the classical notion of generalized perfect and quasi-perfect codes to channels defined over some finite dimensional complex Hilbert output space. The resulting optimality conditions depend on the channel considered and on an auxiliary state defined on the output space of the channel. For certain N-qubit classical-quantum channels, we show that codes based on a generalization of Bell states are quasi-perfect and, therefore, they feature the smallest error probability among all codes of the same blocklength and cardinality.This work was supported in part by the European Research Council (ERC) under Grant 714161; in part by the Agencia Estatal de Investigación, Ministerio de Ciencia e Innovación, the Spanish Government, under Grant RED2018-102668-T, Grant PID2019-104958RB-C41, and Grant PID2020-116683GB-C21; and in part by the Catalan Government, within the ERDF Program of Catalunya, under Grant 2017 SGR 578 AGAUR and Grant 001-P001644 QuantumCAT.Peer ReviewedInstitute of Electrical and Electronics Engineers (IEEE)20222022-09-0120222022-09-29journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/373658https://dx.doi.org/10.1109/TIT.2022.3170868reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-104958RB-C41 AVANCES EN CODIFICACION Y PROCESADO DE SEÑAL PARA LA SOCIEDAD DIGITALopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3736582026-05-27T15:37:01Z
dc.title.none.fl_str_mv Generalized perfect codes for symmetric classical-quantum channels
title Generalized perfect codes for symmetric classical-quantum channels
spellingShingle Generalized perfect codes for symmetric classical-quantum channels
Blasco Coll, Andreu
Quantum communication
Error-correcting codes (Information theory)
Codes
Error probability
Quantum channels
Channel capacity
Quantum system
Task analysis
Quantum state
Comunicació quàntica
Codis correctors d'errors (Teoria de la informació)
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
title_short Generalized perfect codes for symmetric classical-quantum channels
title_full Generalized perfect codes for symmetric classical-quantum channels
title_fullStr Generalized perfect codes for symmetric classical-quantum channels
title_full_unstemmed Generalized perfect codes for symmetric classical-quantum channels
title_sort Generalized perfect codes for symmetric classical-quantum channels
dc.creator.none.fl_str_mv Blasco Coll, Andreu
Vázquez Vilar, Gonzalo
Rodríguez Fonollosa, Javier|||0000-0002-0136-2586
author Blasco Coll, Andreu
author_facet Blasco Coll, Andreu
Vázquez Vilar, Gonzalo
Rodríguez Fonollosa, Javier|||0000-0002-0136-2586
author_role author
author2 Vázquez Vilar, Gonzalo
Rodríguez Fonollosa, Javier|||0000-0002-0136-2586
author2_role author
author
dc.subject.none.fl_str_mv Quantum communication
Error-correcting codes (Information theory)
Codes
Error probability
Quantum channels
Channel capacity
Quantum system
Task analysis
Quantum state
Comunicació quàntica
Codis correctors d'errors (Teoria de la informació)
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
topic Quantum communication
Error-correcting codes (Information theory)
Codes
Error probability
Quantum channels
Channel capacity
Quantum system
Task analysis
Quantum state
Comunicació quàntica
Codis correctors d'errors (Teoria de la informació)
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
description We define a new family of codes for symmetric classical-quantum channels and establish their optimality. To this end, we extend the classical notion of generalized perfect and quasi-perfect codes to channels defined over some finite dimensional complex Hilbert output space. The resulting optimality conditions depend on the channel considered and on an auxiliary state defined on the output space of the channel. For certain N-qubit classical-quantum channels, we show that codes based on a generalization of Bell states are quasi-perfect and, therefore, they feature the smallest error probability among all codes of the same blocklength and cardinality.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-09-01
2022
2022-09-29
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/373658
https://dx.doi.org/10.1109/TIT.2022.3170868
url https://hdl.handle.net/2117/373658
https://dx.doi.org/10.1109/TIT.2022.3170868
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-104958RB-C41 AVANCES EN CODIFICACION Y PROCESADO DE SEÑAL PARA LA SOCIEDAD DIGITAL
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers (IEEE)
publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers (IEEE)
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869406056970452992
score 15,301603

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