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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/65914
Ver los metadatos del registro completo
id |
CONICETDig_d4e74dcfcbba6a25aa78b621762639c8 |
---|---|
oai_identifier_str |
oai:ri.conicet.gov.ar:11336/65914 |
network_acronym_str |
CONICETDig |
repository_id_str |
3498 |
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 Técnicas2025-09-29T10:20:01Zoai: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:34982025-09-29 10:20:02.051CONICET 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 |
_version_ |
1844614176503234560 |
score |
13.070432 |