Local quantum protocols for separable measurements with many parties

TL;DR

This paper extends a method for implementing bipartite separable measurements via LOCC to multi-party scenarios, automatically determining measurement order and identifying limitations of LOCC implementation.

Contribution

It generalizes a previous bipartite protocol to multi-party systems and reveals conditions where LOCC cannot exactly implement certain measurements.

Findings

Protocol automatically determines party measurement order.

Certain rank-1 local operators prevent finite-round LOCC implementation.

Generalization applies to any number of parties.

Abstract

In a recent paper \cite{mySEPvsLOCC}, we showed how to construct a quantum protocol for implementing a bipartite, separable quantum measurement using only local operations on subsystems and classical communication between parties (LOCC) within any fixed number of rounds of communication, whenever such a protocol exists. Here, we generalize that construction to one that applies for any number of parties. One important observation is that the construction automatically determines the ordering of the parties' measurements, overcoming a significant apparent difficulty in designing protocols for more than two parties. We also present various other results about LOCC, including showing that if, in any given measurement operator of the separable measurement under consideration, the local parts for two different parties are rank-1 operators that are not repeated in any other measurement operator of the measurement, then this separable measurement cannot be exactly implemented by LOCC in any finite number of rounds.