two different situations for the implementation of the entangler are discussed). Two conductors, characterized by some scattering matrix, connect the terminals 3 and 4 of the entangler with the exit leads 1 and 2 so to carry the two particles belonging to each pair into two different spatially separated reservoirs. The electron counting is performed in leads 1 and 2 for electrons with spin aligned along the local spin-quantization axis at angles $\theta_1$ and $\theta_2$. Detection is realized by means of spin-selective counters, [*i.e.*]{} by counting electrons with the projection of the spin along a given local quantization-axis. In analogy with the optical case we say that the analyzer is not present when the electron counting is spin-insensitive (electrons are counted irrespective of their spin direction).

In Section \[derivation\] we present the derivation of the CH inequality for the FCS and in Section \[scatt\] we resume, for completeness, the relation between FCS and the scattering matrix $S$.

Derivation of the CH inequality {#derivation}
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The basic object for the formulation of the CH inequality is the joint probability $P(Q_1,Q_2)$ for transferring a number of $Q_1$ and $Q_2$ electronic charges into leads $1$ and $2$ over an observation time $t$. We 