Locally distinguishing a maximally entangled basis using shared entanglement

TL;DR

This paper derives the optimal success probability for distinguishing maximally entangled basis states using local operations and shared entanglement, showing that PPT and separable measurements offer no advantage over LOCC.

Contribution

It provides an exact formula linking success probability to the fully entangled fraction and demonstrates the optimality of a teleportation-based LOCC protocol.

Findings

Success probability equals the fully entangled fraction of the resource state.

PPT and separable measurements do not outperform LOCC in this task.

Bounds are established for incomplete maximally entangled bases.

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.