Remark: Necessary accessible-input correction

Equality of the target two-packet marginals alone is insufficient for this theorem if the apparatus also receives other modes or spectators. Those systems could carry $x$, or their correlations with the packets could depend on $x$. The shared capture acts on ${\mathfrak{v}}_L$, not only on $\mathrm{ran}H$. A label dependence in the orthogonal participating modes can change captured records even when ${\rho }_{12}$ is fixed.

For a radiation-only ideal channel acting exclusively on the target pair, equality of its two-packet inputs does suffice. This distinction prevents a side-channel signal from being renamed microscopic radiation recovery.