The gate-only allowance

A state-specific gate fidelity is not the hypothesis in this corollary. The allowance must hold for the complete local channel, including arbitrary extensions by the other route registers and the untouched reference.

Compatible per-step CPTP channels also constitute a model assumption. Arbitrary time-correlated environmental memory is not automatically covered by local channel benchmarks. Such memory must be included in a declared complete interface on which the comparison maps and error estimates actually hold.