Ruminations on Matrix Convexity and the Strong Subadditivity of Quantum Entropy

10/19/2022

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by   Michael Aizenman, et al.

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The familiar second derivative test for convexity is shown to yield a useful tool also in the context of matrix-valued functions. We demonstrate its applicability 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.