  Correlated photons produced by spontaneous parametric down-conversion are an
essential tool for quantum communication, especially suited for long-distance
connections. To have a reasonable count rate after all the losses in the
propagation and the filters needed to improve the coherence, it is convenient
to increase the intensity of the laser that pumps the non-linear crystal. By
doing so, however, the importance of the four-photon component of the
down-converted field increases, thus degrading the quality of two-photon
interferences. In this paper, we present an easy derivation of this nuisance
valid for any form of entanglement generated by down-conversion, followed by a
full study of the problem for time-bin entanglement. We find that the
visibility of two-photon interferences decreases as V=1-2\rho, where \rho is,
in usual situations, the probability per pulse of creating a detectable photon
pair. In particular, the decrease of V is independent of the coherence of the
four-photon term. Thanks to the fact that \rho can be measured independently of
V, the experimental verification of our prediction is provided for two
different configuration of filters.
