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The non-linearity of a conditional photon-counting measurement can be used to`de-Gaussify' a Gaussian state of light. Here we present and experimentallydemonstrate a technique for photon number resolution using only homodynedetection. We then apply this technique to inform a conditional measurement;unambiguously reconstructing the statistics of the non-Gaussian one and twophoton subtracted squeezed vacuum states. Although our photon numbermeasurement relies on ensemble averages and cannot be used to preparenon-Gaussian states of light, its high efficiency, photon number resolvingcapabilities, and compatibility with the telecommunications band make itsuitable for quantum information tasks relying on the outcomes of mean values.

Photon number discrimination without a photon counter and its application to reconstructing non-Gaussian states