Locally distinguishing a maximally entangled basis using shared entanglement

Abstract

We consider the problem of distinguishing between the elements of a bipartite maximally entangled orthonormal basis using local operations and classical communication (LOCC) and a partially entangled state acting as a resource. We derive an exact formula for the optimum success probability and find that it corresponds to the fully entangled fraction of the resource state. The derivation consists of two steps: First, we consider a relaxation of the problem by replacing LOCC with positive-partial-transpose (PPT) measurements and establish an upper bound on the success probability as the solution of a semidefinite program, and then show that this upper bound is achieved by a teleportation-based LOCC protocol. This further implies that separable and PPT measurements provide no advantage over LOCC for this task. We also present lower and upper bounds on the success probability for distinguishing the elements of an incomplete orthonormal maximally entangled basis in the same setup.