Processor analogy

An $N$-cell processor coherently scrambles a prepared pure input with a fixed unitary and releases its cells one by one. The receiver stores all cells as quantum systems. Under the additional Haar ensemble, the exact mean entropy is the Page curve. Globally the computation remains reversible.

Installing Enter on every released cell changes the returned type to classical strings. The same apparatus now has the monotone record entropy (eq:recordmean) and the permanent quantum-recovery obstruction. Retaining coherent measurement environments would declare a different, larger quantum access interface.