  Photon triplet generation based on third-order spontaneous parametric
down-conversion remains as an experimental challenge. The challenge stems from
the trade-offs between source brightness and instrument noise. This work
presents a probability theory of coincidence detection to address the detection
limit in source characterization. We use Bayes' theorem to model instruments as
a noisy communication channel and apply statistical inference to identify the
minimum detectable coincidence rate. A triplet generation rate of 1-100 Hz is
required for source characterization performed over 1-72 hours using
superconducting nanowire single-photon detectors.
