New Paper out in CMP

Don’t miss out on our latest CMP paper. We recently derived extensions of the Golden-Thompson inequality to arbitrarily many matrices. We show how spectral pinching and complex interpolation theory can be used to prove matrix inequalities. Such inequalities sharpen our understanding of the laws of quantum mechanics.

by Philipp Kammerlander
CMP

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."

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