\rho \right],$$ defining a set of correlations $\mathcal{Q}$ where $M_a^x$ and $M_b^y $ describe measurement operators and $\rho$ is the density operator describing the joint physical system shared by Alice and Bob. Bell’s theorem [@PhysicsPhysiqueFizika.1.195] shows that there are quantum distributions of the form incompatible with the classical description given by , the phenomenon known as quantum nonlocality that can be witnessed by the violation of the CHSH inequality [@PhysRevLett.23.880] $$\label{chsh}
\mathrm{CHSH}= E_{00}+E_{01}+E_{10}-E_{11} \leq 2$$ that in quantum case can achieve $\mathrm{CHSH}= 2 \sqrt{2}$ where $E_{xy}=P(a=b \vert xy)-P(a \neq b \vert xy)$.

A third possible description is to wonder what are the implications on the correlation arising from imposing special relativity to this Bell experiment. Because of the space-like separation between the parties, we see that the statistics observed locally by one of the parties should be completely independent of whatever choice of measurement the other party is doing, otherwise they could communicate superluminally. Mathematically, this is described by following set of linear constraints on the probabilities, known as non-signalling (NS) conditions: $$\begin{aligned}
\label{pns}
& & p(a\vert x) = \sum_{b} p(a,b\vert x,y) =  \sum_{b} p(a,b\vert x,y^{\prime}) \\ \nonumber
& & p(b\vert y) = \sum_{a} p(a,b\vert x,y) = \sum_{a} p(a,b\vert x^{\prime},y),\end{aligned}$$ 