Four-photon correlations of the output radiation of a parametric amplifier with a vacuum at the input are considered for an arbitrary parametric gain coefficient. Such states are interpreted in the literature as four-photon states. It is shown that the fourth-order correlation function for such states in the limit of a small number of photons has an asymptotics typical of two-photon states. Nevertheless, even in the "classical" limit of high intensities, the level of four-photon correlations, i.e., the value of the normalized fourth-order correlation function, is substantially greater than that for coherent and even thermal fields.
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