A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy

Abstract

We consider the following trace function on n-tuples of positive operators: \Phi_p(A_1,A_2,...,A_n) = Trace (\sum_{j=1}^n A_j^p)^{1/p} and prove that it is jointly concave for 0 2, \Phi_p is neither convex nor concave. We conjecture that \Phi_p is convex for 1