Detector Click Floor Boundary Scan - Quantum Mechanics IV: Photons, Interferometers, and Optical Qubits Step by Step

Detector efficiency moves clicked counts across a floor. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Detector clicks must meet a count floor

Arriving photons stay fixed while the efficiency gate changes.

m=N_{\text{click}}-N_{\min}

Three efficiencies bracket the click floor

Two-thirds efficiency exactly meets the click floor; three-quarters passes it.

\begin{array}{c|c|c|c}\eta&N_{\text{click}}&m&\text{gate}\\\frac{1}{2}&6&-2&\text{fail}\\\frac{2}{3}&8&0&\text{pass}\\\frac{3}{4}&9&1&\text{pass}\\\end{array}

The high-efficiency row clears the floor

Clicked plus missed still closes the arrival ledger.

m=1\quad \text{pass}