  We investigate the entanglement and the R\'enyi entropies of two electronic
leads connected by a quantum point contact. For non-interacting electrons, the
entropies can be related to the cumulants of the full counting statistics of
transferred charge which in principle are measurable. We consider the
entanglement entropy generated by operating the quantum point contact as a
quantum switch which is opened and closed in a periodic manner. Using a
numerically exact approach we analyze the conditions under which a logarithmic
growth of the entanglement entropy predicted by conformal field theory should
be observable in an electronic conductor. In addition, we consider clean
single-particle excitations on top of the Fermi sea (levitons) generated by
applying designed pulses to the leads. We identify a Hong-Ou-Mandel-like
suppression of the entanglement entropy by interfering two levitons on a
quantum point contact tuned to half transmission.
