defining a set of correlations $\mathcal{NS}$. Strikingly, there are non-signalling correlation beyond what can be achieved with quantum theory [@popescu1994quantum]. In short, we know that these $3$ sets of correlations respect the following strict inclusion relation: $\mathcal{L} \subsetneq \mathcal{Q} \subsetneq \mathcal{NS}$.

The sets $\mathcal{L}$ and $\mathcal{NS}$ are polytopes, convex sets described by a finite number of extremal points or equivalently a finitely many facets (linear inequalities). In the CHSH scenario, the extremal points of the $\mathcal{NS}$ set have been fully characterized [@PhysRevA.71.022101], consisting of 8 extreme nonlocal points and 16 extreme local points described below. In a Bell scenario we restrict our attention to the probability distribution, regardless of the internal working of the measurement and state preparation devices. For this reason, it is typical to refer to correlations (alternatively, probability distributions) simply as boxes.

-   **PR-box $PR(ab|xy)$**: a no-signaling correlation that maximally violates the CHSH inequality or one of its symmetries. There are 8 of such boxes: $$\nonumber
            PR^{\mu\nu\sigma}(ab|xy)=\frac{1}{2}\delta_{a\oplus b,xy\oplus\mu x\oplus\nu y\oplus \sigma},$$ where $\delta_{[.],[.]}$ representing the Dirac’s delta.

-   **Local-box $L_{\alpha\beta\gamma\theta}$**: there are 16 deterministic local boxes that can be parametrized as: $$\nonumber
        L_{\alpha\beta\gamma\theta}(ab|xy)=\delta_{a,\alpha x\oplus\beta}\delta_{b,\gamma y\oplus \theta}.$$

In the CHSH scenario, any nonlocal distribution can be decomposed as 