Proposition: Access monotonicity

Message-independent CPTP restriction of the accessible output cannot improve unrestricted recovery:

For consistent coherent radiation prefixes, ${ϵ}_{\mathrm{rec}}(t+1)\le {ϵ}_{\mathrm{rec}}(t)$.

Proof. Every decoder after ${\mathcal{A}}_t$ is a decoder for the original output by composition. For prefixes, a later decoder may discard the new block and use an earlier optimal decoder.