Abstract

We give a finite-sample, calibration-aware protocol for certifying a specified deterministic quantum-memory decoder. A logical Bell input and the three correlations $X\otimes X$, $Y\otimes Y$, and $Z\otimes Z$ produce confidence bounds $F_L\le F_e\le F_U$ on the normalized logical Choi overlap. Under the stated contract, with coverage at least $1-\alpha$, an identified target qubit channel has half-diamond error in

where $b$ is a separately justified half-diamond transfer allowance. For direct certification of the implemented laboratory channel, $b=0$. The upper bound controls every input and untouched reference; it does not establish decoder optimality.

We prove bounded-score Hoeffding and exact binomial procedures, calibration-bias conversions, complete failure accounting, and channel-confidence-region refinements. A supplied execution report for the supplementary version-1 script records coverage of all 140 simulated datasets: 20 repetitions for each of seven channels, with 40 shots per setting. It reports zero invalid acceptances at error threshold $0.1$. We show, however, that this sample count cannot accept that threshold even on perfect data; the absence of invalid acceptances therefore does not exercise an informative high-accuracy acceptance regime. The reported identity-channel upper endpoint is approximately $0.8226864813$, correcting a numerical interpretation in the report. Exact rational example endpoints are archived in the manuscript. The execution is supplied evidence, not an independent rerun. No laboratory calibration, laboratory data, device-independent guarantee, or gravitational identification is claimed.