The non-locality of n noisy Popescu-Rohrlich boxes

Details The non-locality of n noisy Popescu-Rohrlich boxes The non-locality of n noisy Popescu-Rohrlich boxes

2008-11-11

arxiv.org/abs/0811.1649v2

J. Phys. A: Math. Theor. 43 465305 (2010)

Physics

Quantum Physics

14 pages, v2: published version

Scientific paper

10.1088/1751-8113/43/46/465305

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.

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