  Gaussian boson sampling is a promising scheme for demonstrating a quantum
computational advantage using photonic states that are accessible in a
laboratory and, thus, offer scalable sources of quantum light. In this
contribution, we study two-point photon-number correlation functions to gain
insight into the interference of Gaussian states in optical networks. We
investigate the characteristic features of statistical signatures which enable
us to distinguish classical from quantum interference. In contrast to the
typical implementation of boson sampling, we find additional contributions to
the correlators under study which stem from the phase dependence of Gaussian
states and which are not observable when Fock states interfere. Using the first
three moments, we formulate the tools required to experimentally observe
signatures of quantum interference of Gaussian states using two outputs only.
By considering the current architectural limitations in realistic experiments,
we further show that a statistically significant discrimination between quantum
and classical interference is possible even in the presence of loss, noise, and
a finite photon-number resolution. Therefore, we formulate and apply a
theoretical framework to benchmark the quantum features of Gaussian boson
sampling under realistic conditions.
