Open-System Cross Scans

Leakage Fraction Three-Row Scan

retained count budgets

Leakage is easier to audit when the lost fraction is scanned across exact rows. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

One tenth leakage keeps ninety shots

The input ledger is 80 zero and 20 one. With leakage fraction 1/10, the lost row is 8 plus 2, so 90 shots remain for readout.

8+2=10,Nkept=908+2=10,\quad N_{\text{kept}}=90
Leakage scan rowThe kept and lost bars close per state.9/10kept1/10lost9/10kept1/10lostleakage budget

One fifth leakage is the original audit row

At leakage fraction 1/5, the kept counts are 64 zero and 16 one, while lost counts total 20.

64+16=80,Nlost=2064+16=80,\quad N_{\text{lost}}=20
Leakage scan rowThe middle row matches the capstone audit.4/5kept1/5lost4/5kept1/5lostleakage budget

Three tenths leakage leaves seventy shots

Increasing leakage to 3/10 gives lost counts 24 and 6. The retained readout budget falls to 70 shots.

24+6=30,Nkept=7024+6=30,\quad N_{\text{kept}}=70
Leakage scan rowThree rows show leakage as a retained-count scan.7/10kept3/10lost7/10kept3/10lostleakage budget