the free variable probabilities to zero.

As shown in [@PhysRevA.99.032106], nonlocal faces can give rise to quantum voids, faces where all nonlocal points are of a postquantum nature. Non-signalling faces of dimension four and smaller are all quantum voids, as well as some of the faces of dimension five and six. These are the sets we will focus throughout out the paper.

Nonlocality distillation and wirings {#sec:NLdist}
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Representing the correlations as a box with inputs and outputs, a nonlocality distillation protocol can be basically understood as a wiring among two boxes, where for instance the outcomes of the first box can be used as the input for the second one. If we wire two distant distributions as $W(p(ab|xy),p^{\prime}(ab|xy))$ we obtain a new distribution $q(ab|xy)$ given by: $$\begin{aligned}
         \label{defwiring}
              & & q(ab|xy) = W(p(ab|xy),p^{\prime}(ab|xy))\\
             \nonumber
             & & =\sum_{a_1,a_2,x_1,x_2,b_1,b_2,y_1,y_2=0}^{1} \chi_x(a,a_1,a_2,x_1,x_2)\chi_y(b,b_1,b_2,y_1,y_2)\cdot \\ \nonumber
             & &\cdot p(a_1b_1|x_1y_1)p^{\prime}(a_2b_2|x_2y_2)
         \end{aligned}$$ where $\chi_x(a,a_1,a_2,x_1,x_2)$ represents the wiring performed locally by Alice and $\chi_y(b,b_1,b_2,y_1,y_2)$ the wiring performed by Bob. Here $x_i$ and $y_j$ are respectively $i$th and $j$th inputs to Alice and Bob’s boxes, and $a_i$ and $b_j$ are the outcomes from respective boxes, $a$ and $b$ are the final respective outputs of Alice and Bob; since two 