Corollary: Identical marginals, different recovery tasks

The experiments $(\eta ,\lambda )=(1,1)$ and $(1,0)$ have identical Bell-input accessible density matrices and therefore identical accessible occupation probabilities, purity, and all observables of that marginal.

Their optimal recovery errors are nevertheless $0$ and $1/2$, their decoded reference concurrences are $1$ and $0$, and their reference–accessible mutual informations are $2$ and $1$, respectively.

Proof. Apply Theorem thm:fullNoise at the two endpoints.