Local approximation of multipartite quantum measurements

TL;DR

This paper establishes a necessary condition for implementing quantum measurements via LOCC protocols, including asymptotic cases, and applies it to solve longstanding problems in state distinguishability.

Contribution

It introduces a unifying geometric condition for asymptotic LOCC and uses it to resolve open questions about state distinguishability.

Findings

Certain unextendible product bases cannot be distinguished by LOCC even asymptotically

The new condition generalizes and clarifies previous results on LOCC implementability

The approach provides an intuitive geometric understanding of LOCC limitations

Abstract

We provide a necessary condition that a quantum measurement can be implemented by the class of protocols known as Local Operations and Classical Communication, or LOCC, including when an error is allowed but must vanish in the limit of an infinite number of rounds, a case referred to as asymptotic LOCC. Our condition unifies, extends, and provides an intuitive, geometric justification for previous results on asymptotic LOCC. We use our condition to answer a variety of long-standing, unsolved problems, including for distinguishability of certain sets of states by LOCC. These include various classes of unextendible product bases, for which we prove they cannot be distinguished by LOCC even when infinite resources are available and asymptotically vanishing error is allowed.