Correlation constraints and the Bloch geometry of two qubits

We present an inequality on the purity of a bipartite state depending solely on the length difference of the local Bloch vectors. For two qubits this inequality is tight for all marginal states and so extends the previously known solution for the two-qubit marginal problem. With this inequality we c...

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Detalles Bibliográficos
Autores: Morelli, S., Eltschka, C., Huber, M., Siewert, J.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1747
Acceso en línea:http://hdl.handle.net/20.500.11824/1747
Access Level:acceso abierto
Palabra clave:Quantum Information
Quantum state space
Entanglement
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spelling Correlation constraints and the Bloch geometry of two qubitsMorelli, S.Eltschka, C.Huber, M.Siewert, J.Quantum InformationQuantum state spaceEntanglementWe present an inequality on the purity of a bipartite state depending solely on the length difference of the local Bloch vectors. For two qubits this inequality is tight for all marginal states and so extends the previously known solution for the two-qubit marginal problem. With this inequality we construct a three-dimensional Bloch model of the two-qubit quantum state space in terms of Bloch lengths, providing a pleasing visualization of this high-dimensional state space. This allows to characterize quantum states by a strongly reduced set of parameters and to investigate the interplay between local properties of the marginal systems and global properties encoded in the correlations.202420242024info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1747reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://doi.org/10.1103/PhysRevA.109.012423info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/CEX2021-001142-Sinfo:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2022-2025info:eu-repo/grantAgreement/Gobierno Vasco/IKUR/Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/17472026-06-19T12:47:47Z
dc.title.none.fl_str_mv Correlation constraints and the Bloch geometry of two qubits
title Correlation constraints and the Bloch geometry of two qubits
spellingShingle Correlation constraints and the Bloch geometry of two qubits
Morelli, S.
Quantum Information
Quantum state space
Entanglement
title_short Correlation constraints and the Bloch geometry of two qubits
title_full Correlation constraints and the Bloch geometry of two qubits
title_fullStr Correlation constraints and the Bloch geometry of two qubits
title_full_unstemmed Correlation constraints and the Bloch geometry of two qubits
title_sort Correlation constraints and the Bloch geometry of two qubits
dc.creator.none.fl_str_mv Morelli, S.
Eltschka, C.
Huber, M.
Siewert, J.
author Morelli, S.
author_facet Morelli, S.
Eltschka, C.
Huber, M.
Siewert, J.
author_role author
author2 Eltschka, C.
Huber, M.
Siewert, J.
author2_role author
author
author
dc.subject.none.fl_str_mv Quantum Information
Quantum state space
Entanglement
topic Quantum Information
Quantum state space
Entanglement
description We present an inequality on the purity of a bipartite state depending solely on the length difference of the local Bloch vectors. For two qubits this inequality is tight for all marginal states and so extends the previously known solution for the two-qubit marginal problem. With this inequality we construct a three-dimensional Bloch model of the two-qubit quantum state space in terms of Bloch lengths, providing a pleasing visualization of this high-dimensional state space. This allows to characterize quantum states by a strongly reduced set of parameters and to investigate the interplay between local properties of the marginal systems and global properties encoded in the correlations.
publishDate 2024
dc.date.none.fl_str_mv 2024
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1747
url http://hdl.handle.net/20.500.11824/1747
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://doi.org/10.1103/PhysRevA.109.012423
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/CEX2021-001142-S
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2022-2025
info:eu-repo/grantAgreement/Gobierno Vasco/IKUR/
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
reponame_str BIRD. BCAM's Institutional Repository Data
collection BIRD. BCAM's Institutional Repository Data
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