  Optical quantum protocols are reliant on the production of highly pure single
photons. However, most parametric heralded single photon sources possess
spectral correlations, limiting the purity of the produced photon. The most
common method for restoring the purity is with narrowband spectral filtering,
which comes at the cost of reducing the rate of heralding detection. Here, we
characterize this trade-off analytically for a large class of parametric
sources. It is possible to achieve up to 20% heralding success probabilities
with 90% heralded photon purities.
