Remark: Conservation and its limits

The autonomous total energy $H$ and total excitation number are conserved. In general $[H,H_0]\ne 0$: photons of frequency $\nu$ exchange with a source of bare energy ${\omega }_0$.

On the prepared code,

Thus the initial product state is not generally a total-energy eigenstate, although its initial bare energy is sharp.

No work-free preparation, autonomous collector, or energy-conserving decoder is constructed. The conserved total energy is not a black-hole mass ledger.