Quantum Distance Measures Based upon Classical Symmetric Csiszár Divergences

Autores
Bussandri, Diego; Osán, Tristán Martín
Año de publicación
2023
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We introduce a new family of quantum distances based on symmetric Csiszár divergences, a class of distinguishability measures that encompass the main dissimilarity measures between probability distributions. We prove that these quantum distances can be obtained by optimizing over a set of quantum measurements followed by a purification process. Specifically, we address in the first place the case of distinguishing pure quantum states, solving an optimization of the symmetric Csiszár divergences over von Neumann measurements. In the second place, by making use of the concept of purification of quantum states, we arrive at a new set of distinguishability measures, which we call extended quantum Csiszár distances. In addition, as it has been demonstrated that a purification process can be physically implemented, the proposed distinguishability measures for quantum states could be endowed with an operational interpretation. Finally, by taking advantage of a well-known result for classical Csiszár divergences, we show how to build quantum Csiszár true distances. Thus, our main contribution is the development and analysis of a method for obtaining quantum distances satisfying the triangle inequality in the space of quantum states for Hilbert spaces of arbitrary dimension.
Fil: Bussandri, Diego. 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; 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
CSISZÁR DIVERGENCES
DISTINGUISHABILITY
HELLINGER DISTANCE
JENSEN–SHANNON DIVERGENCE
QUANTUM METRICS
TRACE DISTANCE
TRIANGULAR DISCRIMINATION
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:11336/226303
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/226303
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Quantum Distance Measures Based upon Classical Symmetric Csiszár DivergencesBussandri, DiegoOsán, Tristán MartínCSISZÁR DIVERGENCESDISTINGUISHABILITYHELLINGER DISTANCEJENSEN–SHANNON DIVERGENCEQUANTUM METRICSTRACE DISTANCETRIANGULAR DISCRIMINATIONhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We introduce a new family of quantum distances based on symmetric Csiszár divergences, a class of distinguishability measures that encompass the main dissimilarity measures between probability distributions. We prove that these quantum distances can be obtained by optimizing over a set of quantum measurements followed by a purification process. Specifically, we address in the first place the case of distinguishing pure quantum states, solving an optimization of the symmetric Csiszár divergences over von Neumann measurements. In the second place, by making use of the concept of purification of quantum states, we arrive at a new set of distinguishability measures, which we call extended quantum Csiszár distances. In addition, as it has been demonstrated that a purification process can be physically implemented, the proposed distinguishability measures for quantum states could be endowed with an operational interpretation. Finally, by taking advantage of a well-known result for classical Csiszár divergences, we show how to build quantum Csiszár true distances. Thus, our main contribution is the development and analysis of a method for obtaining quantum distances satisfying the triangle inequality in the space of quantum states for Hilbert spaces of arbitrary dimension.Fil: Bussandri, Diego. 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; 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; ArgentinaMolecular Diversity Preservation International2023-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/226303Bussandri, Diego; Osán, Tristán Martín; Quantum Distance Measures Based upon Classical Symmetric Csiszár Divergences; Molecular Diversity Preservation International; Entropy; 25; 6; 6-2023; 1-161099-4300CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/1099-4300/25/6/912info:eu-repo/semantics/altIdentifier/doi/10.3390/e25060912info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:52:55Zoai:ri.conicet.gov.ar:11336/226303instacron: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 09:52:55.943CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Quantum Distance Measures Based upon Classical Symmetric Csiszár Divergences
title Quantum Distance Measures Based upon Classical Symmetric Csiszár Divergences
spellingShingle Quantum Distance Measures Based upon Classical Symmetric Csiszár Divergences
Bussandri, Diego
CSISZÁR DIVERGENCES
DISTINGUISHABILITY
HELLINGER DISTANCE
JENSEN–SHANNON DIVERGENCE
QUANTUM METRICS
TRACE DISTANCE
TRIANGULAR DISCRIMINATION
title_short Quantum Distance Measures Based upon Classical Symmetric Csiszár Divergences
title_full Quantum Distance Measures Based upon Classical Symmetric Csiszár Divergences
title_fullStr Quantum Distance Measures Based upon Classical Symmetric Csiszár Divergences
title_full_unstemmed Quantum Distance Measures Based upon Classical Symmetric Csiszár Divergences
title_sort Quantum Distance Measures Based upon Classical Symmetric Csiszár Divergences
dc.creator.none.fl_str_mv Bussandri, Diego
Osán, Tristán Martín
author Bussandri, Diego
author_facet Bussandri, Diego
Osán, Tristán Martín
author_role author
author2 Osán, Tristán Martín
author2_role author
dc.subject.none.fl_str_mv CSISZÁR DIVERGENCES
DISTINGUISHABILITY
HELLINGER DISTANCE
JENSEN–SHANNON DIVERGENCE
QUANTUM METRICS
TRACE DISTANCE
TRIANGULAR DISCRIMINATION
topic CSISZÁR DIVERGENCES
DISTINGUISHABILITY
HELLINGER DISTANCE
JENSEN–SHANNON DIVERGENCE
QUANTUM METRICS
TRACE DISTANCE
TRIANGULAR DISCRIMINATION
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 introduce a new family of quantum distances based on symmetric Csiszár divergences, a class of distinguishability measures that encompass the main dissimilarity measures between probability distributions. We prove that these quantum distances can be obtained by optimizing over a set of quantum measurements followed by a purification process. Specifically, we address in the first place the case of distinguishing pure quantum states, solving an optimization of the symmetric Csiszár divergences over von Neumann measurements. In the second place, by making use of the concept of purification of quantum states, we arrive at a new set of distinguishability measures, which we call extended quantum Csiszár distances. In addition, as it has been demonstrated that a purification process can be physically implemented, the proposed distinguishability measures for quantum states could be endowed with an operational interpretation. Finally, by taking advantage of a well-known result for classical Csiszár divergences, we show how to build quantum Csiszár true distances. Thus, our main contribution is the development and analysis of a method for obtaining quantum distances satisfying the triangle inequality in the space of quantum states for Hilbert spaces of arbitrary dimension.
Fil: Bussandri, Diego. 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; 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 We introduce a new family of quantum distances based on symmetric Csiszár divergences, a class of distinguishability measures that encompass the main dissimilarity measures between probability distributions. We prove that these quantum distances can be obtained by optimizing over a set of quantum measurements followed by a purification process. Specifically, we address in the first place the case of distinguishing pure quantum states, solving an optimization of the symmetric Csiszár divergences over von Neumann measurements. In the second place, by making use of the concept of purification of quantum states, we arrive at a new set of distinguishability measures, which we call extended quantum Csiszár distances. In addition, as it has been demonstrated that a purification process can be physically implemented, the proposed distinguishability measures for quantum states could be endowed with an operational interpretation. Finally, by taking advantage of a well-known result for classical Csiszár divergences, we show how to build quantum Csiszár true distances. Thus, our main contribution is the development and analysis of a method for obtaining quantum distances satisfying the triangle inequality in the space of quantum states for Hilbert spaces of arbitrary dimension.
publishDate 2023
dc.date.none.fl_str_mv 2023-06
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/11336/226303
Bussandri, Diego; Osán, Tristán Martín; Quantum Distance Measures Based upon Classical Symmetric Csiszár Divergences; Molecular Diversity Preservation International; Entropy; 25; 6; 6-2023; 1-16
1099-4300
CONICET Digital
CONICET
url http://hdl.handle.net/11336/226303
identifier_str_mv Bussandri, Diego; Osán, Tristán Martín; Quantum Distance Measures Based upon Classical Symmetric Csiszár Divergences; Molecular Diversity Preservation International; Entropy; 25; 6; 6-2023; 1-16
1099-4300
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/1099-4300/25/6/912
info:eu-repo/semantics/altIdentifier/doi/10.3390/e25060912
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 Molecular Diversity Preservation International
publisher.none.fl_str_mv Molecular Diversity Preservation International
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 13.070432

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