Several exact efficiency gates show detected and missed photons as one count ledger.
Several exact efficiency gates show detected and missed photons as one count ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Half efficiency clicks six of twelve
The detector receives 12 photons. Efficiency 1/2 gives 6 clicked and 6 missed.
12⋅21=6,6+6=12
Two-thirds efficiency clicks eight of twelve
Efficiency 2/3 sends 8 photons to clicked and 4 to missed.
12⋅32=8,8+4=12
Three-quarters efficiency clicks nine of twelve
Efficiency 3/4 gives 9 clicked photons and 3 missed photons.