Phase-space representations of symmetric informationally complete positive-operator-valued-measure fiducial states

Autores
Saraceno, Marcos; Ermann, Leonardo; Cormick, Maria Cecilia
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The problem of finding symmetric informationally complete positive-operator-valued-measures (SIC-POVMs) has been solved numerically for all dimensions d up to 67 [A. J. Scott and M. Grassl, J. Math. Phys. 51, 042203 (2010)JMAPAQ0022-248810.1063/1.3374022], but a general proof of existence is still lacking. For each dimension, it was shown that it is possible to find a SIC-POVM that is generated from a fiducial state upon application of the operators of the Heisenberg-Weyl group. We draw on the numerically determined fiducial states to study their phase-space features, as displayed by the characteristic function and the Wigner, Bargmann, and Husimi representations, adapted to a Hilbert space of finite dimension. We analyze the phase-space localization of fiducial states, and observe that the SIC-POVM condition is equivalent to a maximal delocalization property. Finally, we explore the consequences in phase space of the conjectured Zauner symmetry. In particular, we construct a Hermitian operator commuting with this symmetry that leads to a representation of fiducial states in terms of eigenfunctions with definite semiclassical features.
Fil: Saraceno, Marcos. Comisión Nacional de Energía Atómica; Argentina. Universidad Nacional de San Martín. Escuela de Ciencia y Tecnología; Argentina
Fil: Ermann, Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica; Argentina
Fil: Cormick, Maria Cecilia. 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
Quantum Information
Quantum Chaos
SIC-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:11336/65914
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Phase-space representations of symmetric informationally complete positive-operator-valued-measure fiducial statesSaraceno, MarcosErmann, LeonardoCormick, Maria CeciliaQuantum InformationQuantum ChaosSIC-POVMhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The problem of finding symmetric informationally complete positive-operator-valued-measures (SIC-POVMs) has been solved numerically for all dimensions d up to 67 [A. J. Scott and M. Grassl, J. Math. Phys. 51, 042203 (2010)JMAPAQ0022-248810.1063/1.3374022], but a general proof of existence is still lacking. For each dimension, it was shown that it is possible to find a SIC-POVM that is generated from a fiducial state upon application of the operators of the Heisenberg-Weyl group. We draw on the numerically determined fiducial states to study their phase-space features, as displayed by the characteristic function and the Wigner, Bargmann, and Husimi representations, adapted to a Hilbert space of finite dimension. We analyze the phase-space localization of fiducial states, and observe that the SIC-POVM condition is equivalent to a maximal delocalization property. Finally, we explore the consequences in phase space of the conjectured Zauner symmetry. In particular, we construct a Hermitian operator commuting with this symmetry that leads to a representation of fiducial states in terms of eigenfunctions with definite semiclassical features.Fil: Saraceno, Marcos. Comisión Nacional de Energía Atómica; Argentina. Universidad Nacional de San Martín. Escuela de Ciencia y Tecnología; ArgentinaFil: Ermann, Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica; ArgentinaFil: Cormick, Maria Cecilia. 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 Society2017-03info: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/11336/65914Saraceno, Marcos; Ermann, Leonardo; Cormick, Maria Cecilia; Phase-space representations of symmetric informationally complete positive-operator-valued-measure fiducial states; American Physical Society; Physical Review A; 95; 3; 3-2017; 32102-321132469-9934CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.95.032102info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.032102info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:52:38Zoai:ri.conicet.gov.ar:11336/65914instacron: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:34982025-10-22 11:52:39.155CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Phase-space representations of symmetric informationally complete positive-operator-valued-measure fiducial states
title Phase-space representations of symmetric informationally complete positive-operator-valued-measure fiducial states
spellingShingle Phase-space representations of symmetric informationally complete positive-operator-valued-measure fiducial states
Saraceno, Marcos
Quantum Information
Quantum Chaos
SIC-POVM
title_short Phase-space representations of symmetric informationally complete positive-operator-valued-measure fiducial states
title_full Phase-space representations of symmetric informationally complete positive-operator-valued-measure fiducial states
title_fullStr Phase-space representations of symmetric informationally complete positive-operator-valued-measure fiducial states
title_full_unstemmed Phase-space representations of symmetric informationally complete positive-operator-valued-measure fiducial states
title_sort Phase-space representations of symmetric informationally complete positive-operator-valued-measure fiducial states
dc.creator.none.fl_str_mv Saraceno, Marcos
Ermann, Leonardo
Cormick, Maria Cecilia
author Saraceno, Marcos
author_facet Saraceno, Marcos
Ermann, Leonardo
Cormick, Maria Cecilia
author_role author
author2 Ermann, Leonardo
Cormick, Maria Cecilia
author2_role author
author
dc.subject.none.fl_str_mv Quantum Information
Quantum Chaos
SIC-POVM
topic Quantum Information
Quantum Chaos
SIC-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 The problem of finding symmetric informationally complete positive-operator-valued-measures (SIC-POVMs) has been solved numerically for all dimensions d up to 67 [A. J. Scott and M. Grassl, J. Math. Phys. 51, 042203 (2010)JMAPAQ0022-248810.1063/1.3374022], but a general proof of existence is still lacking. For each dimension, it was shown that it is possible to find a SIC-POVM that is generated from a fiducial state upon application of the operators of the Heisenberg-Weyl group. We draw on the numerically determined fiducial states to study their phase-space features, as displayed by the characteristic function and the Wigner, Bargmann, and Husimi representations, adapted to a Hilbert space of finite dimension. We analyze the phase-space localization of fiducial states, and observe that the SIC-POVM condition is equivalent to a maximal delocalization property. Finally, we explore the consequences in phase space of the conjectured Zauner symmetry. In particular, we construct a Hermitian operator commuting with this symmetry that leads to a representation of fiducial states in terms of eigenfunctions with definite semiclassical features.
Fil: Saraceno, Marcos. Comisión Nacional de Energía Atómica; Argentina. Universidad Nacional de San Martín. Escuela de Ciencia y Tecnología; Argentina
Fil: Ermann, Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica; Argentina
Fil: Cormick, Maria Cecilia. 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 The problem of finding symmetric informationally complete positive-operator-valued-measures (SIC-POVMs) has been solved numerically for all dimensions d up to 67 [A. J. Scott and M. Grassl, J. Math. Phys. 51, 042203 (2010)JMAPAQ0022-248810.1063/1.3374022], but a general proof of existence is still lacking. For each dimension, it was shown that it is possible to find a SIC-POVM that is generated from a fiducial state upon application of the operators of the Heisenberg-Weyl group. We draw on the numerically determined fiducial states to study their phase-space features, as displayed by the characteristic function and the Wigner, Bargmann, and Husimi representations, adapted to a Hilbert space of finite dimension. We analyze the phase-space localization of fiducial states, and observe that the SIC-POVM condition is equivalent to a maximal delocalization property. Finally, we explore the consequences in phase space of the conjectured Zauner symmetry. In particular, we construct a Hermitian operator commuting with this symmetry that leads to a representation of fiducial states in terms of eigenfunctions with definite semiclassical features.
publishDate 2017
dc.date.none.fl_str_mv 2017-03
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/11336/65914
Saraceno, Marcos; Ermann, Leonardo; Cormick, Maria Cecilia; Phase-space representations of symmetric informationally complete positive-operator-valued-measure fiducial states; American Physical Society; Physical Review A; 95; 3; 3-2017; 32102-32113
2469-9934
CONICET Digital
CONICET
url http://hdl.handle.net/11336/65914
identifier_str_mv Saraceno, Marcos; Ermann, Leonardo; Cormick, Maria Cecilia; Phase-space representations of symmetric informationally complete positive-operator-valued-measure fiducial states; American Physical Society; Physical Review A; 95; 3; 3-2017; 32102-32113
2469-9934
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.95.032102
info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.032102
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 12.982451

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