Complete failures

If the accessible process is an instrument $\{{\mathcal{I}}_z{\}}_z$, and branch $z$ has a declared CPTP output operation $D_z$, the deterministic returned channel is

It is CPTP because compositions and sums preserve complete positivity and ${\sum }_z{\mathcal{I}}_z$ is trace preserving.

Successful branches alone are not renormalized into a deterministic certificate. Loss can be completed by a declared fixed output, or retained as a flag in a different output type. These are different tasks, not interchangeable conventions CheungEn02B,CheungEn02C,CheungEm05B.