When a quantum measurement can be implemented locally ... and when it cannot

TL;DR

This paper investigates the distinction between LOCC protocols and separable measurements in quantum systems, providing a method to construct LOCC protocols for most separable measurements and explicitly identifying those that cannot be implemented locally.

Contribution

It introduces a construction method for LOCC protocols to realize separable measurements and explicitly demonstrates cases where LOCC implementation is impossible.

Findings

Most separable measurements can be implemented via LOCC using the proposed method.

The paper explicitly identifies separable measurements that cannot be realized by LOCC.

Provides a systematic way to distinguish between implementable and non-implementable measurements.

Abstract

Local operations on subsystems and classical communication between parties (LOCC) constitute the most general protocols available on spatially separated quantum systems. Every LOCC protocol implements a separable generalized measurement -- a complete measurement for which every outcome corresponds to a tensor product of operators on individual subsystems -- but it is known that there exist separable measurements that cannot be implemented by LOCC. A longstanding problem in quantum information theory is to understand the difference between LOCC and the full set of separable measurements. In this paper, we show how to construct an LOCC protocol to implement an arbitrary separable measurement, except that with those measurements for which no LOCC protocol exists, the method shows explicitly that this is the case.