Distinguishability of complete and unextendible product bases

Abstract

It is not always possible to distinguish multipartite orthogonal states if only local operation and classical communication (LOCC) are allowed. We prove that we cannot distinguish the states of an unextendible product basis (UPB) by LOCC even when infinite resources (infinite-dimensional ancillas, infinite number of operations). Moreover we give a necessary and sufficient condition for the LOCC distinguishability of complete product bases.

added necessary and sufficient condition for complete product bases, example Lagarias-Shor ten-parties complete basis