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One of the most fascinating consequences of quantum theory is non-locality,i.e., the fact that the behavior under measurements of (spatially separated)parts of a system can have a correlation unexplainable by shared classicalinformation. Note that at the same time, these correlations are non-signalingand do not allow for message transmission. Popescu and Rohrlich have defined anon-local box as a basic building block of non-locality and initiated asystematic study of non-local correlations and their applications. They leftopen, however, whether any non-signaling correlation can be simulated by suchnon-local boxes. We show that the answer is yes with respect to arbitrarilyaccurate approximations.

The Universality of Non-Local Boxes