### Abstract

Strong subadditivity of von Neumann entropy, proved in 1973 by Lieb and Ruskai, is a cornerstone of quantum coding theory. All other known inequalities for entropies of quantum systems may be derived from it. I will describe some work with Andreas Winter in which we prove a new inequality for the von Neumann entropy which is independent of strong subadditivity. This work sheds light on extremal types of entanglement for multi-party quantum states.