Characterizing electron entanglement in multi-mode mesoscopic conductors

We show that current correlations at the exit ports of a beam sphtter can be used to detect electronic entanglement for a fairly general input state. First, we demonstrate that multimode entanglement of electrons in a mesoscopic conductor can be detected by a measurement of the zero-frequency current correlations in an electronic Hong-Ou-Mandel interferometer By this means, one can further establish a lower bound to the entanglement of formation of two-electron input states. Second, we include the situation where electron pairs can enter the beam splitter from the same port or be separated due to backscattering. The proposed scheme allows to discriminate between particle-number and mode entanglement.