Complete channels and their complements

This is the established exact error-correction structure KnillLaflamme, also stated in the supplied Hawk03-A, Hawk04-A/B, En07-A/C, and Oai290-A interfaces CheungHawk03A,CheungHawk04A,CheungHawk04B, CheungEn07A,CheungEn07C,CheungOai290A. No model-specific source channel is imported.

In finite dimensions decoder Choi matrices form a compact set. Consequently a nonconstant complete complement implies ${\epsilon }_{\mathrm{rec}}(\mathcal{N})>0$, not merely failure of an attained exact decoder. The dimension bound is a Hilbert-space count, not an area law.