Significance of heralding in spontaneous parametric down-conversion

Single photons exhibit nonclassical, counterintuitive behavior that can be exploited in the developing field of quantum technology. They are needed for various applications such as quantum key distribution, optical quantum information processing, quantum computing, intensity measurement standards, and others yet to be discovered in this developing field. This drives the current intensive research into the realization of true deterministic sources of single photons on demand. Lacking such a source, many researchers default to the well-established workhorse: spontaneous parametric down-conversion that generates entangled signal-idler pairs. Since this source is thermal statistical in nature, it is common to use a detected idler photon to herald the production of a signal photon. The need exists to determine the quality of the single photons generated in the heralded signal beam. Quite often, the literature reports a heralded second-order coherence function of the signal photons conditioned on the idler photons using readily available single-photon detectors. In this work we examine the applicability of this technique to single-photon characterization and the consequences of the fact that the most commonly used single-photon detectors are not photon-number resolving. Our results show that this method using non-photon-resolving detectors can only be used to characterize the signal-idler correlations rather than the nature of the signal-photon state alone.