organized as follows: in the next Section we motivate our approach to the problem, derive the CH inequality and express the joint probabilities needed in the CH inequality in terms of the scattering properties of the mesoscopic conductor. Section \[results\] is devoted to the discussion of the results. We first consider the idealized situation where an incoming flux of fully entangled electrons is injected into the mesoscopic region. Then we move on to analyze actual setups. Interacting electrons are not necessary to have an entangled state, we show that a three terminal normal device is enough to lead to violation of the CH inequality. For completeness we also consider the case where entanglement is produced by Andreev reflection. In the last Section we present the conclusions and a brief summary of this work.

CH inequality for the full counting statistics
==============================================

Electron Full Counting Statistics (FCS) refers to the probability that a given number of electrons has traversed, in a time $t$, a mesoscopic conductor. In the long time limit the first and the second moment of the probability distribution are related to the average current and noise, respectively. The reason for which we resort to FCS for analyzing electronic 