  We show that a one dimensional device supporting a pair of Majorana bound
states at its ends can produce remarkable Hanbury-Brown Twiss like interference
effects between well separated Dirac fermions of pertinent energies. We find
that the simultaneous scattering of two incoming electrons or two incoming
holes from the Majorana bound states leads exclusively to an electron-hole
final state. This "anti-bunching" in electron-hole internal pseudospin space
can be detected through current-current correlations. Further, we show that, by
scattering appropriate spin polarized electrons from the Majorana bound states,
one can engineer a non-local entangler of electronic spins for quantum
information applications. Both the above phenomena should be observable in
diverse physical systems enabling to detect the presence of low energy Majorana
modes.
