Corrections retained from version 1

Pure-target trace distance is an inequality. For a generally mixed state $\rho$ and rank-one projector $P$,

The upper inequality is not generally an equality. It is an equality when both states are pure.

Replacement benchmarks depend on the decoder task. A qubit replacement channel has optimal recovery error $3/4$. A specified decoder returning a fixed pure state can have error $1$.

Confidence is a repeated-experiment guarantee. The theorem bounds the probability of an invalid certificate. It does not assign a posterior probability to a channel after observing a particular dataset.

The reference and tested channel must be identified. An uncalibrated reference operation can compensate a memory error. Preparation, reference isolation, measurement, stationarity, and failure accounting are part of the contract.