I’m happy to announce that my first ever paper has finally been uploaded on the arXiv. In it, we develop closed-form expressions for the moments and cumulants of Gaussian states when measured in the photon-number basis. arxiv.org/abs/2212.06067
We finally performed a Monte Carlo simulation using matrices sampled at random from the Haar measure to compare cumulants of different single-mode Gaussian states fed into an interferometer.
We showed, based on our expression for cumulants, that squashed states are significantly better than thermal states at mimicking photon-number cumulants of lossy and lossless squeezed states, while thermal states perform poorly.