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⋅12=6,6+6=1212\cdot\frac{1}{2}=6,\quad 6+6=12
Detector efficiency scan rowClicked and missed bars close the count ledger.1/2clicked1/2misseddetector

Two-thirds efficiency clicks eight of twelve

Efficiency 2/3 sends 8 photons to clicked and 4 to missed.

12⋅23=8,8+4=1212\cdot\frac{2}{3}=8,\quad 8+4=12
Detector efficiency scan rowThe total arrivals stay fixed while efficiency changes.2/3clicked1/3misseddetector

Three-quarters efficiency clicks nine of twelve

Efficiency 3/4 gives 9 clicked photons and 3 missed photons.

12⋅34=9,9+3=1212\cdot\frac{3}{4}=9,\quad 9+3=12
Detector efficiency scan rowEfficiency is a gate on counts, not a detector label.3/4clicked1/4misseddetector