The non-locality of n noisy Popescu-Rohrlich boxes

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 $1-\epsilon$, is of order $\Theta ({\epsilon }^{\lceil n/2\rceil })$ in the isotropic, and equal to $(3\epsilon {)}^n$ in the maximally biased case.

14 pages, v2: published version

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• Quantifying the randomness of copies of noisy Popescu-Rohrlich correlations
• Events in quantum mechanics are maximally non-absolute