Certificates, comparisons, and the resulting release

For a fixed finite network, channel equality can be tested on all matrix units and all classical input blocks. Checking a few input states is weaker.

With half-diamond normalization $d_{\diamond }(\Phi ,\Psi )=\frac{1}{2}\Vert \Phi -\Psi {\Vert }_{\diamond }$, complete channel errors telescope under composition:

Consequently a relay's ideal law gap $1$ remains at least $1-2e$ if both implemented laws are within total variation $e$ of ideal.