Asymptotics of Quantum Relative Entropy From Representation Theoretical Viewpoint

Abstract

In this paper it was proved that the quantum relative entropy $D(σ\| ρ)$ can be asymptotically attained by Kullback Leibler divergences of probabilities given by a certain sequence of POVMs. The sequence of POVMs depends on $ρ$, but is independent of the choice of $σ$.