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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/203385
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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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1844613645241155584 |
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13.070432 |