Entanglement Monogamy via Multivariate Trace Inequalities

Berta, M; Tomamichel, M

Entanglement Monogamy via Multivariate Trace Inequalities

Berta, M Tomamichel, M

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Publisher:: SPRINGER
Publication Type:: Journal Article
Citation:: Communications in Mathematical Physics, 2024, 405, (2)
Issue Date:: 2024-02-01

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Field	Value	Language
dc.contributor.author	Berta, M
dc.contributor.author	Tomamichel, M https://orcid.org/0000-0001-5410-3329
dc.date.accessioned	2025-03-06T03:41:41Z
dc.date.available	2025-03-06T03:41:41Z
dc.date.issued	2024-02-01
dc.identifier.citation	Communications in Mathematical Physics, 2024, 405, (2)
dc.identifier.issn	0010-3616
dc.identifier.issn	1432-0916
dc.identifier.uri	http://hdl.handle.net/10453/185530
dc.description.abstract	Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite systems. Here, we derive variational formulas for relative entropies based on restricted measurements of multipartite quantum systems. By combining these with multivariate matrix trace inequalities, we recover and sometimes strengthen various existing entanglement monogamy inequalities. In particular, we give direct, matrix-analysis-based proofs for the faithfulness of squashed entanglement by relating it to the relative entropy of entanglement measured with one-way local operations and classical communication, as well as for the faithfulness of conditional entanglement of mutual information by relating it to the separably measured relative entropy of entanglement. We discuss variations of these results using the relative entropy to states with positive partial transpose, and multipartite setups. Our results simplify and generalize previous derivations in the literature that employed operational arguments about the asymptotic achievability of information-theoretic tasks.
dc.language	English
dc.publisher	SPRINGER
dc.relation.ispartof	Communications in Mathematical Physics
dc.relation.isbasedon	10.1007/s00220-023-04920-5
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0101 Pure Mathematics, 0105 Mathematical Physics, 0206 Quantum Physics
dc.subject.classification	Mathematical Physics
dc.subject.classification	4902 Mathematical physics
dc.subject.classification	4904 Pure mathematics
dc.subject.classification	5107 Particle and high energy physics
dc.title	Entanglement Monogamy via Multivariate Trace Inequalities
dc.type	Journal Article
utslib.citation.volume	405
utslib.for	0101 Pure Mathematics
utslib.for	0105 Mathematical Physics
utslib.for	0206 Quantum Physics
pubs.organisational-group	University of Technology Sydney
pubs.organisational-group	University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	University of Technology Sydney/UTS Groups
pubs.organisational-group	University of Technology Sydney/UTS Groups/Centre for Quantum Software and Information (QSI)
pubs.organisational-group	University of Technology Sydney/UTS Groups/Centre for Cyber Security and Privacy (CCSP)
pubs.organisational-group	University of Technology Sydney/UTS Groups/Centre for Quantum Software and Information (QSI)/Centre for Quantum Software and Information (QSI) Associate Members
utslib.copyright.status	closed_access	*
dc.date.updated	2025-03-06T03:41:40Z
pubs.issue	2
pubs.publication-status	Published
pubs.volume	405
utslib.citation.issue	2

Abstract:

Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite systems. Here, we derive variational formulas for relative entropies based on restricted measurements of multipartite quantum systems. By combining these with multivariate matrix trace inequalities, we recover and sometimes strengthen various existing entanglement monogamy inequalities. In particular, we give direct, matrix-analysis-based proofs for the faithfulness of squashed entanglement by relating it to the relative entropy of entanglement measured with one-way local operations and classical communication, as well as for the faithfulness of conditional entanglement of mutual information by relating it to the separably measured relative entropy of entanglement. We discuss variations of these results using the relative entropy to states with positive partial transpose, and multipartite setups. Our results simplify and generalize previous derivations in the literature that employed operational arguments about the asymptotic achievability of information-theoretic tasks.

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http://hdl.handle.net/10453/185530