What the numerical and experimental tests can establish

For a specified decoded channel, let its Bell overlap be

A Bell-projector test always gives the error lower witness $1-F$. A validated lower bound $F\ge F_0$ also gives

by the pure-target fidelity–trace-distance inequality FuchsVanDeGraaf. Hence the dimension-explicit upper certificate is

High Bell overlap is therefore useful, but its conversion to a uniform diamond certificate must retain the dimension factor or use a sharper independently proved channel estimate.

Repeated calibrated preparations and measurements can estimate such quantities. They are not one-run tomography of an unknown diary. Statistical bounds must state their confidence level; numerical feasibility and physical preparation/receiver errors remain separate.