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Due to their strict photon-number correlation, the twin beams produced inparametric down-conversion (PDC) work well for heralded state generation.Often, however, this state manipulation is distorted by the optical losses inthe herald and by the higher photon-number contributions inevitable in the PDCprocess. In order to find feasible figures of merit for characterizing theheralded states, we investigate their normalized factorial moments of thephoton number that can be accessed regardless of the optical losses in thedetection. We then perform a measurement of the joint photon statistics of twinbeams from a semiconductor Bragg-reflection waveguide with transition-edgesensors acting as photon-number-resolving detectors. We extract thephoton-number parity of heralded single photons in a loss-tolerant fashion byutilizing the moment generating function. The photon-number parity is highlypracticable in quantum state characterization, since it takes into account thecomplete photon-number content of the target state.

Photon-number parity of heralded single photons from a Bragg-reflection waveguide reconstructed loss-tolerantly via moment generating function