  In this work we investigate the probabilities of detecting single- and
multi-photon coherent states on InGaAs/InP sine-gated and free-run
single-photon avalanche diodes. As a result, we conclude that multi-photon
state detection cannot be regarded as independent events of absorption of
individual single-photon states. However, if a greater number of states are
one- and two-photon, then an Independent model is permissible. We conclude that
physical processes must occur in the diode structure, determining the
correlation when several photons are absorbed simultaneously. We present two
models that we can use to describe photon interactions in a structure. The
Dependent model is based on an increase/decrease in the probability of
detecting an n-th photon upon an unfortunate detection of an (n-1)-th photon in
an n-photon state and is well physically grounded; The Empirical model offers a
simple and accurate empirical relationship.
