Detector efficiency is modeled as a count gate that splits incoming photons into clicked and missed ledgers. The split is exact only for the stated incoming count and rational efficiency; real detectors add dark counts, afterpulsing, dead time, threshold settings, wavelength dependence, and counting uncertainty.
Detector efficiency is represented as an exact clicked-versus-missed count split. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Efficiency is a rational count gate
The detector receives 12 photons. Efficiency 3/4 means the clicked count is 9.
12⋅43=9
Missed counts remain in the ledger
The remaining count is 3 missed photons, and 9 plus 3 closes back to 12.