now consider the violation of the CH inequality as a function of the transmitted charges. We notice that the CH inequality is not violated for the off-diagonal terms of the distributions (when $Q_1 \neq Q_2$), meaning that one really needs to look at “coincidences”. Therefore we discuss the case $Q_1=Q_2\equiv Q<M$ (remember that the no-enhancement assumption is satisfied only for $T\leq T_{\text{max}}(Q)$). In Fig. \[S:Q&lt;M\] we plot the quantity ${\cal S}_{CH}$ for $M=20$ as a function of $\Theta$ and different values of $Q$. The transmission $T$ is fixed at the highest allowed value by the no-enhancement assumption, which corresponds to the smallest $Q$ considered $T_{\text{max}}(Q=1)=0.06917$. Fig. \[S:Q&lt;M\] shows that the largest positive value of ${\cal S}_{CH}$ and the widest range of angles corresponding to positive ${\cal S}_{CH}$ occur for $Q=1$, [*i.e.*]{} for a joint probability relative to the detection of a single pair. One should not conclude that, in order to detect the violation of the CH inequality, only very small values of the transmitted charge should be taken. We have in fact considered $T=T_{\text{max}}$ relative to $Q=1$ and the maximum violation, for given $M$ and $Q$, always occurs at $T=T_{\text{max}}$. In order to get the largest violation of the 