Bipartite Units of Non-Locality

TL;DR

This paper demonstrates that bipartite nonlocal correlations can be approximated arbitrarily well using shared PR boxes, establishing them as asymptotic units of bipartite nonlocality, and explores limitations in multipartite cases.

Contribution

It proves PR boxes serve as asymptotic units for bipartite nonlocality and analyzes the constraints of simulating multipartite nonlocal correlations.

Findings

PR boxes can simulate any bipartite nonlocal correlation arbitrarily accurately.

Non-adaptive strategies have limited accuracy in multipartite correlation simulation.

The error probability in arbitrary strategies scales at least as c/n for some constant c.

Abstract

Imagine a task in which a group of separated players aim to simulate a statistic that violates a Bell inequality. Given measurement choices the players shall announce an output based solely on the results of local operations -- which they can discuss before the separation -- on shared random data and shared copies of a so-called unit correlation. In the first part of this article we show that in such a setting the simulation of any bipartite correlation, not containing the possibility of signaling, can be made arbitrarily accurate by increasing the number of shared Popescu-Rohrlich (PR) boxes. This establishes the PR box as a simple asymptotic unit of bipartite nonlocality. In the second part we study whether this property extends to the multipartite case. More generally, we ask if it is possible for separated players to asymptotically reproduce any nonsignaling statistic by local operations on bipartite unit correlations. We find that non-adaptive strategies are limited by a constant accuracy and that arbitrary strategies on n resource correlations make a mistake with a probability greater or equal to c/n, for some constant c.