specific classes of correlations. The difficulty relies on the fact that the number of possible wirings involved in a nonlocality distillation protocol increases very fast. As proven in [@PhysRevA.73.012101], the set of possible protocols define a convex set, the extremal points of which are finitely many deterministic wirings. However, already at simplest possible Bell scenario, the CHSH scenario with two parties and two dichotomic measurements per party [@PhysRevA.89.042106], there are $82^4 = 45.212.176$ deterministic wirings, reason why we have seen slow progress in this research direction.

On the more fundamental side, nonlocality distillation also plays a key role in the search for information-theoretical principles able to characterize the set of quantum correlations. It is known that special relativity alone cannot single out the quantum set, as there are correlation compatible with the non-signalling principle but beyond what can be achieved with quantum theory [@popescu1994quantum]. This has motivated the introduction of several new principles [@pawlowski2009information; @chaves2015information; @navascues2009glance; @fritz2013local; @navascues2015almost; @van2013implausible; @PhysRevLett.96.250401]. However, as noticed in [@PhysRevA.80.062107], whatever principle a physical theory fulfills, the set of correlations it generates should be closed under wirings, implying non trivial constraints on the search for physical principles and the axiomatization of quantum theory [@Lang_2014].

In 