Example: Three required controls

1. $p=0$: the whole radiation channel is a replacement channel. The source and environments retain the message.

2. $p=1,\eta =0$: computational-basis information is fully available collectively, but input coherence is lost to the dephasing environment. The channel is entanglement breaking.

3. $p=1,\eta =1$: the collective radiation permits exact referenced quantum recovery.

The emitted occupation statistics and the individual-cell privacy do not distinguish these three information tasks.