The non-locality of n noisy Popescu-Rohrlich boxes
Matthias Fitzi, Esther H\"anggi, Valerio Scarani, Stefan Wolf

TL;DR
This paper analyzes how the non-locality of noisy Popescu-Rohrlich boxes scales with the number of systems, providing quantitative bounds on their local parts based on noise levels.
Contribution
It introduces a method to quantify the non-locality in multiple noisy PRBs and derives bounds on their local components depending on noise and bias.
Findings
Local part scales as Θ(ε^{ceil(n/2)}) in isotropic case
Local part is (3ε)^n in maximally biased case
Provides quantitative bounds on non-locality in noisy PRBs
Abstract
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 , is of order in the isotropic, and equal to in the maximally biased case.
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