2017 - T3 - WS3 - Quantum information theory

Collection 2017 - T3 - WS3 - Quantum information theory

Organizer(s) Fawzi, Omar ; Harrow, Aram ; Kerenidis, Iordanis ; Szarek, Stanislaw ; Winter, Andreas

Date(s) 11/12/2017 - 15/12/2017

linked URL https://web.archive.org/web/20201010200040/https://sites.google.com/site/analysisqit2017/

00:00:00 / 00:00:00

4 19

Matrix trace inequalities for quantum entropy

I will present multivariate trace inequalities that extend the Golden-Thompson and Araki-Lieb-Thirring inequalities as well as some logarithmic trace inequalities to arbitrarily many matrices. From our four matrix extension of the Golden–Thompson inequality, I will then deduce various remainder terms for the monotonicity of the quantum relative entropy and strong sub-additivity of the von Neumann entropy in terms of recoverability. The proofs rely on complex interpolation theory as well as asymptotic spectral pinching, providing a transparent approach to treat generic multivariate trace inequalities. Based on [Multivariate Trace Inequalities (with Sutter and Tomamichel)], [Quantum Markov Chains and Logarithmic Trace Inequalities (with Sutter and Tomamichel)], and [On Composite Quantum Hypothesis Testing (with Brandao and Hirche)].

Information about the video

Date of recording 11/12/2017
Date of publication 12/12/2017
Institution IHP
Licence CC BY-NC-ND
Language English
Format MP4

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