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.
Aizenman, M., Cipolloni, G. (2023). Ruminations on matrix convexity and the strong subadditivity of quantum entropy. LETTERS IN MATHEMATICAL PHYSICS, 113(1) [10.1007/S11005-023-01638-2].
Ruminations on matrix convexity and the strong subadditivity of quantum entropy
Cipolloni, Giorgio
2023-01-01
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.File in questo prodotto:
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