  A non-local box is a virtual device that has the following property: given
that Alice inputs a bit at her end of the device and that Bob does likewise, it
produces two bits, one at Alice's end and one at Bob's end, such that the XOR
of the outputs is equal to the AND of the inputs. This box, inspired from the
CHSH inequality, was first proposed by Popescu and Rohrlich to examine the
question: given that a maximally entangled pair of qubits is non-local, why is
it not maximally non-local? We believe that understanding the power of this box
will yield insight into the non-locality of quantum mechanics. It was shown
recently by Cerf, Gisin, Massar and Popescu, that this imaginary device is able
to simulate correlations from any measurement on a singlet state. Here, we show
that the non-local box can in fact do much more: through the simulation of the
magic square pseudo-telepathy game and the Mermin-GHZ pseudo-telepathy game, we
show that the non-local box can simulate quantum correlations that no entangled
pair of qubits can in a bipartite scenario and even in a multi-party scenario.
Finally we show that a single non-local box cannot simulate all quantum
correlations and propose a generalization for a multi-party non-local box. In
particular, we show quantum correlations whose simulation requires an
exponential amount of non-local boxes, in the number of maximally entangled
qubit pairs.
