The Universality of Non‐Local Boxes

One of the most fascinating consequences of quantum theory is non‐locality, i.e., the fact that the measurement outcomes of (spatially separated) parts of a system can have a correlation unexplainable by shared classical information. Note that at the same time, these correlations are non‐signaling and do not allow for message transmission. Popescu and Rohrlich have defined a non‐local box as a “basic building block of non‐locality” and initiated a systematic study of non‐local correlations and their applications. However, they left open the question of whether any non‐signaling correlation can be simulated by such non‐local boxes. We show that the answer is yes with respect to arbitrarily accurate approximations.