On multivariate trace inequalities of Sutter, Berta and Tomamichel
Marius Lemm

TL;DR
This paper analyzes a family of multivariate trace inequalities that extend classical inequalities to multiple matrices using complex powers, with potential applications in quantum information theory.
Contribution
It reformulates multivariate trace inequalities using resolvents and entangled states, facilitating their application in quantum information and perturbation analysis.
Findings
Reformulation of inequalities with resolvents and entangled states
Extension of Lieb's three-matrix inequality to n matrices
Potential applications in quantum information theory, especially in the analysis of the Petz recovery map
Abstract
We consider a family of multivariate trace inequalities recently derived by Sutter, Berta and Tomamichel. These inequalities generalize the Golden-Thompson inequality and Lieb's three-matrix inequality to an arbitrary number of matrices in a way that features complex matrix powers. We show that their inequalities can be rewritten as an -matrix generalization of Lieb's original three-matrix inequality. The complex matrix powers are replaced by resolvents and appropriate maximally entangled states. We expect that the technically advantageous properties of resolvents, in particular for perturbation theory, can be of use in applications of the -matrix inequalities, e.g., for analyzing the rotated Petz recovery map in quantum information theory.
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