Corollary: A separate receiver allowance

Suppose an actual quantum-output receiver gives a channel ${{\mathcal{N}}_t}^{\mathrm{recv}}:C\to R_{\ast }$ with a proved allowance

Then

A specified fixed endpoint decoder has error at most $\min \{1,{\alpha }_t+{\nu }_t+{\epsilon }_{\mathrm{rec}}({\mathcal{N}}_{\ast })\}$. The receiver assumption is not a consequence of an observable probability comparison or a classical count record.

Proof. Apply contraction and the triangle inequality once more to the fixed decoder in Theorem thm:endpoint. Use the endpoint upper bound and the independent constant-decoder cap. The final sentence distinguishes the stated quantum-output channel hypothesis from weaker data.