Figure 1.
Microscopic experiment. If Alice and Bob repeat an experiment many times, each time applying random interactions *X* and *Y* , they can compare their measurement outcomes, make statistics and obtain a set of probabilities *P*(*a*,*b*), the probability of measuring clicks in detectors *D*(*a*),*D*(*b*) when Alice applies an interaction *X*(*a*) and Bob applies an interaction *Y* (*b*). From now on, we will assume that the no-signalling condition holds, i.e. that, for any *X*,*X*′ with *X*≠*X*′, , and, for any *Y*,*Y* ′ with *Y* ≠*Y* ′, . These two conditions just assert that Alice’s choice of measurement setting cannot affect Bob’s statistics and vice versa. Also, the set of marginal probability distributions *P*(*a*,*b*), in general, will not admit a *local hidden variable model*. This means that, in some cases, there will *not* exist a joint probability distribution for all 2*s* possible measurements *P*(*c*_{1},…,*c*_{2s}), such that .