The non-locality of n noisy Popescu-Rohrlich boxes

Abstract

We quantify the amount of non-locality contained in n noisy versions of the so-called Popescu-Rohrlich boxes (PRBs), i.e. bipartite systems violating the CHSH Bell inequality maximally. Following the approach by Elitzur, Popescu and Rohrlich, we measure the amount of non-locality of a system by representing it as a convex combination of a local behaviour, with maximal possible weight, and a non-signalling system. We show that the local part of n systems, each of which approximates a PRB with probability 1 - ε, is of order Θ(ε⌈n/2⌉) in the isotropic, and equal to (3ε)n in the maximally biased case. © 2010 IOP Publishing Ltd.