Proposition: Nested access and entropy

If a later accessible channel admits the earlier one as CPTP postprocessing, then its unrestricted recovery error cannot increase. No corresponding monotonicity holds for quantum subsystem entropy. Restriction of access alone does not imply a Page curve.

Proof. A later decoder can first apply the postprocessing and then an earlier decoder. Quantum entropy can decrease on adding a factor: the first half of a Bell pair has positive entropy, whereas the complete pair is pure. Conversely, a pure product state has zero entropy on every tensor prefix despite the same sequence of increasing access dimensions.