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Ruminations on Matrix Convexity and the Strong Subadditivity of Quantum Entropy (2210.10729v5)
Published 19 Oct 2022 in quant-ph, cond-mat.stat-mech, cs.IT, math-ph, math.IT, and math.MP
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.