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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.