Multivariate Trace Inequalities

Sutter, D; Berta, M; Tomamichel, M

Multivariate Trace Inequalities

Sutter, D Berta, M Tomamichel, M

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Publication Type:: Journal Article
Citation:: Communications in Mathematical Physics, 2017, 352 (1), pp. 37 - 58
Issue Date:: 2017-05-01

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Field	Value	Language
dc.contributor.author	Sutter, D	en_US
dc.contributor.author	Berta, M	en_US
dc.contributor.author	Tomamichel, M https://orcid.org/0000-0001-5410-3329	en_US
dc.date.issued	2017-05-01	en_US
dc.identifier.citation	Communications in Mathematical Physics, 2017, 352 (1), pp. 37 - 58	en_US
dc.identifier.issn	0010-3616	en_US
dc.identifier.uri	http://hdl.handle.net/10453/125316
dc.description.abstract	© 2016, The Author(s). We prove several trace inequalities that extend the Golden–Thompson and the Araki–Lieb–Thirring inequality to arbitrarily many matrices. In particular, we strengthen Lieb’s triple matrix inequality. As an example application of our four matrix extension of the Golden–Thompson inequality, we prove remainder terms for the monotonicity of the quantum relative entropy and strong sub-additivity of the von Neumann entropy in terms of recoverability. We find the first explicit remainder terms that are tight in the commutative case. Our proofs rely on complex interpolation theory as well as asymptotic spectral pinching, providing a transparent approach to treat generic multivariate trace inequalities.	en_US
dc.relation.ispartof	Communications in Mathematical Physics	en_US
dc.relation.isbasedon	10.1007/s00220-016-2778-5	en_US
dc.subject.classification	Mathematical Physics	en_US
dc.title	Multivariate Trace Inequalities	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	352	en_US
utslib.for	0101 Pure Mathematics	en_US
utslib.for	0105 Mathematical Physics	en_US
utslib.for	0206 Quantum Physics	en_US
pubs.embargo.period	Not known	en_US
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/Faculty of Engineering and Information Technology/School of Computer Science
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
utslib.copyright.status	closed_access
pubs.issue	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	352	en_US

Abstract:

© 2016, The Author(s). We prove several trace inequalities that extend the Golden–Thompson and the Araki–Lieb–Thirring inequality to arbitrarily many matrices. In particular, we strengthen Lieb’s triple matrix inequality. As an example application of our four matrix extension of the Golden–Thompson inequality, we prove remainder terms for the monotonicity of the quantum relative entropy and strong sub-additivity of the von Neumann entropy in terms of recoverability. We find the first explicit remainder terms that are tight in the commutative case. Our proofs rely on complex interpolation theory as well as asymptotic spectral pinching, providing a transparent approach to treat generic multivariate trace inequalities.

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http://hdl.handle.net/10453/125316