Proposition: Postprocessing the Em03-F channel

Suppose

For every deterministic radiation-only access channel $\mathcal{A}$ and decoder $\mathcal{D}$,

is entanglement breaking. Its qubit Bell fidelity is at most $1/2$, and its recovery half-diamond error is at least $1/2$.

Proof. The displayed channel remains measure-and-prepare. For a referenced input its output is a sum of positive product operators. Postprocessing on the receiver side preserves separability. A separable two-qubit state has Bell overlap at most $1/2$: the pure-product bound follows by Cauchy–Schwarz and the mixed bound by convexity. The Bell-projector test gives the distance lower bound.