Yet Another Proof of the Joint Convexity of Relative Entropy

12/27/2021

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by   Mary Beth Ruskai, et al.

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The joint convexity of the map (X,A) ↦ X^* A^-1 X, an integral representation of convex operator functions, and an observation of Ando are used to obtain a simple proof of both the joint convexity of relative entropy and a trace convexity result of Lieb. The latter was the key ingredient in the original proof of the strong subadditivity of quantum entropy.