The successor-program correction

The phrase “radiation recovery, then $\mathsf{Enter}$ on $R$” requires a correction. Applying $\mathsf{Enter}$ directly to the radiation register produces a record, not an arbitrary reference-entangled diary. The correct recovery interface is

with quantum return. A prescribed observation may subsequently consume $C_{\mathrm{out}}$. These two target channels are ${\mathrm{id}}_C$ and the chosen measurement channel, respectively.

Likewise, a linear program cannot silently leave a live residual wire out of its return statement. Section sec:programs therefore distinguishes:

• the complete program returning $RB$;

• the local decoder program $R\to C_{\mathrm{out}}$;

• a joint program returning $C_{\mathrm{out}}B$;

• the observer's radiation-only marginal;

• an explicitly added readout-and-drop implementation of that marginal in a finite qubit encoding.

The last implementation is not inferred from the autonomous Hamiltonian.