Title: Ruminations on Matrix Convexity and the Strong Subadditivity of Quantum Entropy
Abstract:

In the context of matrix-valued functions, M to F(M), the second-derivative test of convexity is practically approachable in only few special cases.  Still, by Loewner’s theorem on matrix-monotone and its extension by Kraus to matrix convex-functions F, these few cases essentially cover the range of matrix convexity.  We demonstrate that such relatively simple means allow to establish the celebrated Lieb-Ruskai `73 theorem on the strong sub-additivity of quantum entropy. 
(Joint work with Giorgio Cipolloni.)