Proposition: Access-preserving local unitaries preserve leakage

For

with local output unitaries,

These unitaries may be non-Clifford.

Proof. The residual channel is ${\mathcal{C}}^{\prime }={\mathrm{Ad}}_{U_B}\mathcal{C}$. Replacement states are carried bijectively to their conjugates, and unitary channel distances are invariant. On radiation, a decoder may undo $U_R$, and conversely may prepend it when comparing the two tasks.