Multivariate trace inequalities
File(s)
Published version
Author(s)
Sutter, D
Berta, M
Tomamichel, M
Type
Journal Article
Abstract
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.
Date Issued
2017-05-01
Date Acceptance
2016-08-11
Citation
Communications in Mathematical Physics, 2017, 352 (1), pp.37-58
ISSN
0010-3616
Publisher
Springer Verlag
Start Page
37
End Page
58
Journal / Book Title
Communications in Mathematical Physics
Volume
352
Issue
1
Copyright Statement
© 2016 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Subjects
Science & Technology
Physical Sciences
Physics, Mathematical
Physics
CONDITIONAL MUTUAL INFORMATION
GOLDEN-THOMPSON INEQUALITY
RELATIVE ENTROPY
QUANTUM
LIEB
STATES
math-ph
math-ph
cs.IT
math.IT
math.MP
quant-ph
Mathematical Physics
0101 Pure Mathematics
0105 Mathematical Physics
0206 Quantum Physics
Publication Status
Published
Date Publish Online
2016-10-18