of system parameters correspond to different such ranges. The quantity ${\cal S}_{CH}$ in Eq.(\[CHin\]) depends on $Q_1$ and $Q_2$ so that the possible violation, or the extent of it, also depends on $Q_1$ and $Q_2$. Given a certain average number $M$ of entangled pairs that have being injected in the time $t$, one can look for the maximum violation as a function of the transmitted charges $Q_1$ and $Q_2$.

Scattering approach to the full counting statistics {#scatt}
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The joint probabilities appearing in Eq.(\[CHin\]) can be determined once the scattering matrix $S$ of the mesoscopic conductor is known. The FCS in electronic systems was first introduced by Levitov [*et al.*]{} in Ref. [@levitov93; @levitov96] in the context of the scattering theory and later on the Keldysh Green function method [@nazarov99] to FCS was developed in Refs.[@nazarov01] (for a review see Refs. [@FCS]). In this paragraph we briefly describe how the FCS is formulated for a mesoscopic conductor in the scattering approach. Within this framework, the transport properties of a metallic phase-coherent structure attached to $n$ reservoirs are determined by the matrix $S$ of scattering amplitudes [@buttiker92]. Such amplitudes are defined through the scattering states describing particles propagating through the leads. 