Visualizing Three-Qubit Entanglement

We present a graphical framework to represent entanglement in three-qubit states. The geometry associated with each entanglement class and type is analyzed, revealing distinct structural features. We explore the connection between this geometric perspective and the tangle, deriving bounds that depen...

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Detalles Bibliográficos
Autores: Benedito, Alfred, Sierra, Germán
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:dnet:digitalcsic_::2ca4582e5e4f2e0e1df6b7525fb7787b
Acceso en línea:http://hdl.handle.net/10261/429396
https://api.elsevier.com/content/abstract/scopus_id/105014521984
Access Level:acceso abierto
Palabra clave:canonical form
entanglement classes
entanglement invariants
entanglement polytope
quantum entanglement
tamgle
three-qubit state
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spelling Visualizing Three-Qubit EntanglementBenedito, AlfredSierra, Germáncanonical formentanglement classesentanglement invariantsentanglement polytopequantum entanglementtamglethree-qubit stateWe present a graphical framework to represent entanglement in three-qubit states. The geometry associated with each entanglement class and type is analyzed, revealing distinct structural features. We explore the connection between this geometric perspective and the tangle, deriving bounds that depend on the entanglement class. Based on these insights, we conjecture a purely geometric expression for both the tangle and Cayley's hyperdeterminant for non-generic states. As an application, we analyze the energy eigenstates of physical Hamiltonians, identifying the sufficient conditions for genuine tripartite entanglement to be robust under symmetry-breaking perturbations and level repulsion effects.We acknowledge financial support from the Spanish MINECO grant PID2021-127726NB-I00, the CSIC Research Platform on Quantum Technologies PTI-001, and the QUANTUM ENIA project Quantum Spain funded through the RTRP-Next Generation program under the framework of the Digital Spain 2026 Agenda. A.B. acknowledges support from the Spanish Ministry of Science, Innovation and Universities grant PRE2022-I0I93I. G.S. also acknowledges partial support from NSF grant PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP), as well as joint sponsorship from the Fulbright Program and the Spanish Ministry of Science, Innovation and Universities.Peer reviewedMinisterio de Ciencia e Innovación (España)Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202620262025info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Publisher's versioninfo:eu-repo/semantics/publishedVersionhttp://hdl.handle.net/10261/429396https://api.elsevier.com/content/abstract/scopus_id/105014521984reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)InglésEntropy (Basel, Switzerland)https://www.mdpi.com/1099-4300/27/8/800Síinfo:eu-repo/semantics/openAccessoai:dnet:digitalcsic_::2ca4582e5e4f2e0e1df6b7525fb7787b2026-05-22T06:33:51Z
dc.title.none.fl_str_mv Visualizing Three-Qubit Entanglement
title Visualizing Three-Qubit Entanglement
spellingShingle Visualizing Three-Qubit Entanglement
Benedito, Alfred
canonical form
entanglement classes
entanglement invariants
entanglement polytope
quantum entanglement
tamgle
three-qubit state
title_short Visualizing Three-Qubit Entanglement
title_full Visualizing Three-Qubit Entanglement
title_fullStr Visualizing Three-Qubit Entanglement
title_full_unstemmed Visualizing Three-Qubit Entanglement
title_sort Visualizing Three-Qubit Entanglement
dc.creator.none.fl_str_mv Benedito, Alfred
Sierra, Germán
author Benedito, Alfred
author_facet Benedito, Alfred
Sierra, Germán
author_role author
author2 Sierra, Germán
author2_role author
dc.contributor.none.fl_str_mv Ministerio de Ciencia e Innovación (España)
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv canonical form
entanglement classes
entanglement invariants
entanglement polytope
quantum entanglement
tamgle
three-qubit state
topic canonical form
entanglement classes
entanglement invariants
entanglement polytope
quantum entanglement
tamgle
three-qubit state
description We present a graphical framework to represent entanglement in three-qubit states. The geometry associated with each entanglement class and type is analyzed, revealing distinct structural features. We explore the connection between this geometric perspective and the tangle, deriving bounds that depend on the entanglement class. Based on these insights, we conjecture a purely geometric expression for both the tangle and Cayley's hyperdeterminant for non-generic states. As an application, we analyze the energy eigenstates of physical Hamiltonians, identifying the sufficient conditions for genuine tripartite entanglement to be robust under symmetry-breaking perturbations and level repulsion effects.
publishDate 2025
dc.date.none.fl_str_mv 2025
2026
2026
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Publisher's version
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/429396
https://api.elsevier.com/content/abstract/scopus_id/105014521984
url http://hdl.handle.net/10261/429396
https://api.elsevier.com/content/abstract/scopus_id/105014521984
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Entropy (Basel, Switzerland)
https://www.mdpi.com/1099-4300/27/8/800
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.198674

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