Bipartite subspaces having no LOCC-distinguishable bases - John Watrous

One of the focuses of the theory of quantum information in recent years has been to understand the powers and limitations of LOCC protocols, which are protocols in which two or more physically separated parties may perform arbitrary local quantum operations and may communicate with one another, but only classically. A particular problem that has been studied in this context is the state distinguishability problem: one of a known finite collection of orthogonal states is shared between two or more parties, and their goal is to determine which of the states it is by means of an LOCC protocol. In this talk I will show that there exist subspaces of bipartite tensor product spaces with the property that no orthonormal basis of the subspace has the property that its elements can be distinguished by means of an LOCC protocol. This fact implies that there exist quantum channels having sub-optimal classical capacity even when the receiver may communicate classically with a third party that represents the channel\'s environment.