The non-locality of n noisy Popescu-Rohrlich boxes

We quantify the amount of non-locality contained in n noisy versions of 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 $Θ(ε^{\lceil n/2\rceil})$ in the isotropic, and equal to $(3ε)^n$ in the maximally biased case.

No reviews yet.

No comments yet.