Ruminations on Matrix Convexity and the Strong Subadditivity of Quantum Entropy
arXiv:2210.10729 · doi:10.1007/s11005-023-01638-2
Abstract
The familiar second derivative test for convexity, combined with resolvent calculus, is shown to yield a useful tool for the study of convex matrix-valued functions. We demonstrate the applicability of this approach on a number of theorems in this field. These include convexity principles which play an essential role in the Lieb-Ruskai proof of the strong subadditivity of quantum entropy.
The published version of this paper includes a local mistake in Eq. (5.7). Posted here are: i) the corresponding Erratum & Addendum (LMP 2024), and ii) a corrected version of the paper with the minor adjustments spelled in (i)