Proposition: Selected output entropy does not identify recovery

There are complete isometric interfaces having identical zero radiation entropy on every pure code input, while their optimal outgoing recovery errors are respectively $1-d^{-2}$ and $0$.

Proof. Take $R\cong B\cong C$ and define

For every pure code input, both accessible outputs are pure and have entropy zero. The first accessible channel is constant, so Proposition prop:featureless gives optimal error $1-d^{-2}$. The second is the identity and has error zero.