Classification of four qubit states and their stabilisers under SLOCC operations

Autores
Dietrich, Heiko; De Graaf, Willem A.; Marrani, Alessio; Origlia, Marcos Miguel
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We classify four qubit states under SLOCC operations, that is, we classify the orbits of the group SL(2,C)4 on the Hilbert space H4=(C2)⊗4 . We approach the classification by realising this representation as a symmetric space of maximal rank. We first describe general methods for classifying the orbits of such a space. We then apply these methods to obtain the orbits in our special case, resulting in a complete and irredundant classification of SL(2,C)4 -orbits on H4 . It follows that an element of (C2)⊗4 is conjugate to an element of precisely 87 classes of elements. Each of these classes either consists of one element or of a parameterised family of elements, and the elements in the same class all have equal stabiliser in SL(2,C)4 . We also present a complete and irredundant classification of elements and stabilisers up to the action of Sym4⋉ SL(2,C)4 where Sym4 permutes the four tensor factors of (C2)⊗4 .
Fil: Dietrich, Heiko. Monash University; Australia
Fil: De Graaf, Willem A.. Universita degli Studi di Trento; Italia
Fil: Marrani, Alessio. Universidad de Murcia; España
Fil: Origlia, Marcos Miguel. Monash University; Australia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Materia
CLASSIFICATION
FOUR QUBIT STATES
LIE ALGEBRA
SLOCC
SYMMETRIC SPACES
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:11336/203385

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network_name_str CONICET Digital (CONICET)
spelling Classification of four qubit states and their stabilisers under SLOCC operationsDietrich, HeikoDe Graaf, Willem A.Marrani, AlessioOriglia, Marcos MiguelCLASSIFICATIONFOUR QUBIT STATESLIE ALGEBRASLOCCSYMMETRIC SPACEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We classify four qubit states under SLOCC operations, that is, we classify the orbits of the group SL(2,C)4 on the Hilbert space H4=(C2)⊗4 . We approach the classification by realising this representation as a symmetric space of maximal rank. We first describe general methods for classifying the orbits of such a space. We then apply these methods to obtain the orbits in our special case, resulting in a complete and irredundant classification of SL(2,C)4 -orbits on H4 . It follows that an element of (C2)⊗4 is conjugate to an element of precisely 87 classes of elements. Each of these classes either consists of one element or of a parameterised family of elements, and the elements in the same class all have equal stabiliser in SL(2,C)4 . We also present a complete and irredundant classification of elements and stabilisers up to the action of Sym4⋉ SL(2,C)4 where Sym4 permutes the four tensor factors of (C2)⊗4 .Fil: Dietrich, Heiko. Monash University; AustraliaFil: De Graaf, Willem A.. Universita degli Studi di Trento; ItaliaFil: Marrani, Alessio. Universidad de Murcia; EspañaFil: Origlia, Marcos Miguel. Monash University; Australia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaIOP Publishing2022-02-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/203385Dietrich, Heiko; De Graaf, Willem A.; Marrani, Alessio; Origlia, Marcos Miguel; Classification of four qubit states and their stabilisers under SLOCC operations; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 55; 9; 11-2-2022; 1-191751-8113CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8121/ac4b13info:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/1751-8121/ac4b13info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2111.05488v1info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:54:04Zoai:ri.conicet.gov.ar:11336/203385instacron: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 09:54:04.468CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Classification of four qubit states and their stabilisers under SLOCC operations
title Classification of four qubit states and their stabilisers under SLOCC operations
spellingShingle Classification of four qubit states and their stabilisers under SLOCC operations
Dietrich, Heiko
CLASSIFICATION
FOUR QUBIT STATES
LIE ALGEBRA
SLOCC
SYMMETRIC SPACES
title_short Classification of four qubit states and their stabilisers under SLOCC operations
title_full Classification of four qubit states and their stabilisers under SLOCC operations
title_fullStr Classification of four qubit states and their stabilisers under SLOCC operations
title_full_unstemmed Classification of four qubit states and their stabilisers under SLOCC operations
title_sort Classification of four qubit states and their stabilisers under SLOCC operations
dc.creator.none.fl_str_mv Dietrich, Heiko
De Graaf, Willem A.
Marrani, Alessio
Origlia, Marcos Miguel
author Dietrich, Heiko
author_facet Dietrich, Heiko
De Graaf, Willem A.
Marrani, Alessio
Origlia, Marcos Miguel
author_role author
author2 De Graaf, Willem A.
Marrani, Alessio
Origlia, Marcos Miguel
author2_role author
author
author
dc.subject.none.fl_str_mv CLASSIFICATION
FOUR QUBIT STATES
LIE ALGEBRA
SLOCC
SYMMETRIC SPACES
topic CLASSIFICATION
FOUR QUBIT STATES
LIE ALGEBRA
SLOCC
SYMMETRIC SPACES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We classify four qubit states under SLOCC operations, that is, we classify the orbits of the group SL(2,C)4 on the Hilbert space H4=(C2)⊗4 . We approach the classification by realising this representation as a symmetric space of maximal rank. We first describe general methods for classifying the orbits of such a space. We then apply these methods to obtain the orbits in our special case, resulting in a complete and irredundant classification of SL(2,C)4 -orbits on H4 . It follows that an element of (C2)⊗4 is conjugate to an element of precisely 87 classes of elements. Each of these classes either consists of one element or of a parameterised family of elements, and the elements in the same class all have equal stabiliser in SL(2,C)4 . We also present a complete and irredundant classification of elements and stabilisers up to the action of Sym4⋉ SL(2,C)4 where Sym4 permutes the four tensor factors of (C2)⊗4 .
Fil: Dietrich, Heiko. Monash University; Australia
Fil: De Graaf, Willem A.. Universita degli Studi di Trento; Italia
Fil: Marrani, Alessio. Universidad de Murcia; España
Fil: Origlia, Marcos Miguel. Monash University; Australia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
description We classify four qubit states under SLOCC operations, that is, we classify the orbits of the group SL(2,C)4 on the Hilbert space H4=(C2)⊗4 . We approach the classification by realising this representation as a symmetric space of maximal rank. We first describe general methods for classifying the orbits of such a space. We then apply these methods to obtain the orbits in our special case, resulting in a complete and irredundant classification of SL(2,C)4 -orbits on H4 . It follows that an element of (C2)⊗4 is conjugate to an element of precisely 87 classes of elements. Each of these classes either consists of one element or of a parameterised family of elements, and the elements in the same class all have equal stabiliser in SL(2,C)4 . We also present a complete and irredundant classification of elements and stabilisers up to the action of Sym4⋉ SL(2,C)4 where Sym4 permutes the four tensor factors of (C2)⊗4 .
publishDate 2022
dc.date.none.fl_str_mv 2022-02-11
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/11336/203385
Dietrich, Heiko; De Graaf, Willem A.; Marrani, Alessio; Origlia, Marcos Miguel; Classification of four qubit states and their stabilisers under SLOCC operations; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 55; 9; 11-2-2022; 1-19
1751-8113
CONICET Digital
CONICET
url http://hdl.handle.net/11336/203385
identifier_str_mv Dietrich, Heiko; De Graaf, Willem A.; Marrani, Alessio; Origlia, Marcos Miguel; Classification of four qubit states and their stabilisers under SLOCC operations; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 55; 9; 11-2-2022; 1-19
1751-8113
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8121/ac4b13
info:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/1751-8121/ac4b13
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2111.05488v1
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 IOP Publishing
publisher.none.fl_str_mv IOP Publishing
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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