  We study the time dependent electron-electron and electron-hole correlations
in a mesoscopic device which is splitting an incident current of free fermions
into two spatially separated particle streams. We analyze the appearance of
entanglement as manifested in a Bell inequality test and discuss its origin in
terms of local spin-singlet correlations already present in the initial channel
and the action of post-selection during the Bell type measurement. The time
window over which the Bell inequality is violated is determined in the
tunneling limit and for the general situation with arbitrary transparencies. We
compare our results with alternative Bell inequality tests based on coincidence
probabilities.
