Lemma: Recovery witnesses

Decoded constant and entanglement-breaking qubit channels have half-diamond error at least $3/4$ and $1/2$, respectively. For a Pauli channel $\Lambda ={\sum }_P{\lambda }_P{\mathrm{Ad}}_P$,

Proof. A constant channel's Bell-input output has Bell overlap $1/4$. A separable two-qubit state has Bell overlap at most $1/2$. Testing the Bell projector gives the lower bounds. For a Pauli channel the Bell errors are orthogonal, giving $1-{\lambda }_I$; the triangle inequality gives the matching upper bound.