  We consider the electronic analog of the Hong-Ou-Mandel interferometer from
quantum optics. In this realistic condensed matter device, single electrons are
injected and travel along opposite chiral edge states of the integer quantum
Hall effect, colliding at a quantum point contact (QPC). We monitor the fate of
the colliding excitations by calculating zero-frequency current correlations at
the output of the QPC. In the simpler case of filling factor $\nu=1$, we
recover the standard result of a dip in the current noise as a function of the
time delay between electron injections. For simultaneous injection, the current
correlations exactly vanish, as dictated by the Pauli principle. This picture
is however dramatically modified when interactions are present, as we show in
the case of a filling factor $\nu=2$. There, each edge state is made out of two
co-propagating channels, leading to charge fractionalization, and ultimately to
decoherence. The latter phenomenon reduces the degree of indistinguishability
between the two electron wavepackets, yielding a reduced contrast in the HOM
signal. This naturally brings about the question of stronger interaction,
offering a natural extension of the present work to the case of fractional
quantum Hall effect where many open and fascinating questions remain.
