Bipartite Units of Non-Locality

Manuel Forster, Stefan Wolf

Published 2008-08-05, updated 2011-11-03Version 4

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.