probability distribution is in general complicated, as one can see in Appendix \[PR\] where such expressions for different systems are reported.

Results
=======

The inequality presented in Eq.(\[CHin\]) can be tested in various multi-terminal mesoscopic conductors. In this Section we present several geometries that can be experimentally realized. In order to get acquainted with the informations that can be retrieved from Eq.(\[CHin\]) we start from an ideal case in which the entangled pair is generated by some [*entangler*]{} in the same spirit as in the works of Refs. [@burkard00; @taddei02]. In Section \[ns\] we shall demonstrate that a normal beam splitter in the absence of interaction is enough to generate entangled pairs of electrons, therefore constituting a simple realization of an entangler. For comparison we also analyze the role of superconductivity in creating spin singlets.

Entangled electrons {#ee}
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In the setup depicted in Fig. \[Ent\] we assume the existence of an entangler that produces electron pairs in the Bell state $${\left|\psi\right\rangle}=\frac{1}{\sqrt{2}} 
\left [a^{\dagger}_{3\uparrow}(E) a^{\dagger}_{4\downarrow}(E) \pm  a^{\dagger}_{3\downarrow}(E)
a^{\dagger}_{4\uparrow} (E)\right ]
{\left|0\right\rangle} ,
\label{st}$$ of spin triplet (upper sign) or spin singlet (lower sign) in the energy range $0<E<eV$. These electrons propagate through the conductors which connect terminals 3 and 4 