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

The nonlinearity of a conditional photon-counting measurement can be used to “de-Gaussify” a Gaussian state of light. Here we present and experimentally demonstrate a technique for photon-number resolution using only homodyne detection. We then apply this technique to inform a conditional measurement, unambiguously reconstructing the statistics of the non-Gaussian one- and two-photon-subtracted squeezed vacuum states. Although our photon-number measurement relies on ensemble averages and cannot be used to prepare non-Gaussian states of light, its high efficiency, photon-number-resolving capabilities, and compatibility with the telecommunications band make it suitable for quantum-information tasks relying on the outcomes of mean values.