Optimal resource states for local state discrimination

TL;DR

This paper investigates the use of shared entanglement as a resource to enhance local distinguishability of quantum states, defining optimal resources and providing explicit protocols for certain multipartite states.

Contribution

It introduces the concept of optimal resource states for local state discrimination and provides explicit protocols for GHZ, Graph states, and bipartite bases.

Findings

Maximally entangled states are optimal for certain bipartite bases.

Explicit local protocols for distinguishing multipartite GHZ and Graph states.

Not all entangled states are useful for local discrimination tasks.

Abstract

We study the problem of locally distinguishing pure quantum states using shared entanglement as a resource. For a given set of locally indistinguishable states, we define a resource state to be useful if it can enhance local distinguishability and optimal if it can distinguish the states as well as global measurements and is also minimal with respect to a partial ordering defined by entanglement and dimension. We present examples of useful resources and show that an entangled state need not be useful for distinguishing a given set of states. We obtain optimal resources with explicit local protocols to distinguish multipartite GHZ and Graph states; and also show that a maximally entangled state is an optimal resource under one-way LOCC to distinguish any bipartite orthonormal basis which contains at least one entangled state of full Schmidt rank.