survival-phase-chain-boundary-scan - Quantum Measurement and Coherence Windows Step by Step

Retained survival counts feed phase visibility before a visible-count gate. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Survival retained shots feed visibility

Each row first closes retained plus lost shots, then uses retained shots as the phase budget input.

N_{\text{visible}}\ge20

Three chained rows show the visible-count boundary

The middle row lands exactly on the visible-count floor; the last row falls below it.

\begin{array}{c|c|c|c}N_{\text{ret}}&N_{\text{coh}}&N_{\text{vis}}&m\\80&60&30&10\\60&40&20&0\\40&10&10&-10\\\end{array}

The final chain fails the visible-count floor

The source budgets still close, but the computed visible count leaves a negative margin.

m=-10\quad \text{fail}