Entanglement marginal problems

We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite programming relaxations of the set of quantum state marginals...

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Autores principales:	Miguel Navascués, Flavio Baccari, Antonio Acín
Formato:	article
Lenguaje:	EN
Publicado:	Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/04860e9e1cfb4bca8f450f9f639b65a3
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id	oai:doaj.org-article:04860e9e1cfb4bca8f450f9f639b65a3
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spelling	oai:doaj.org-article:04860e9e1cfb4bca8f450f9f639b65a32021-11-25T15:24:26ZEntanglement marginal problems2521-327X10.22331/q-2021-11-25-589https://doaj.org/article/04860e9e1cfb4bca8f450f9f639b65a32021-11-01T00:00:00Zhttps://quantum-journal.org/papers/q-2021-11-25-589/pdf/https://doaj.org/toc/2521-327XWe consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite programming relaxations of the set of quantum state marginals admitting a fully separable extension. We connect the completeness of each hierarchy to the resolution of an analog classical marginal problem and thus identify relevant experimental situations where the hierarchies are complete. For finitely many parties on a star configuration or a chain, we find that we can achieve an arbitrarily good approximation to the set of nearest-neighbour marginals of separable states with a time (space) complexity polynomial (linear) on the system size. Our results even extend to infinite systems, such as translation-invariant systems in 1D, as well as higher spatial dimensions with extra symmetries.Miguel NavascuésFlavio BaccariAntonio AcínVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenarticlePhysicsQC1-999ENQuantum, Vol 5, p 589 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Miguel Navascués Flavio Baccari Antonio Acín Entanglement marginal problems
description	We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite programming relaxations of the set of quantum state marginals admitting a fully separable extension. We connect the completeness of each hierarchy to the resolution of an analog classical marginal problem and thus identify relevant experimental situations where the hierarchies are complete. For finitely many parties on a star configuration or a chain, we find that we can achieve an arbitrarily good approximation to the set of nearest-neighbour marginals of separable states with a time (space) complexity polynomial (linear) on the system size. Our results even extend to infinite systems, such as translation-invariant systems in 1D, as well as higher spatial dimensions with extra symmetries.
format	article
author	Miguel Navascués Flavio Baccari Antonio Acín
author_facet	Miguel Navascués Flavio Baccari Antonio Acín
author_sort	Miguel Navascués
title	Entanglement marginal problems
title_short	Entanglement marginal problems
title_full	Entanglement marginal problems
title_fullStr	Entanglement marginal problems
title_full_unstemmed	Entanglement marginal problems
title_sort	entanglement marginal problems
publisher	Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
publishDate	2021
url	https://doaj.org/article/04860e9e1cfb4bca8f450f9f639b65a3
work_keys_str_mv	AT miguelnavascues entanglementmarginalproblems AT flaviobaccari entanglementmarginalproblems AT antonioacin entanglementmarginalproblems
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Entanglement marginal problems

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