Specified quantum errors before assignment

Amplitude damping is explicitly a bath model; each displayed Kraus pair has a unitary system–bath dilation. The pointer assignment isometry was given above. Thus these are complete channels and instruments, rather than unsigned additive “measurement errors.”

For clarity, write $\mathcal{Z}$ for the composition of damping, basis rotation, and spectator evolution. On a ready branch, the selective record map is

where ${\Pi }_j=I_{QS}\otimes |j⟩⟨j{|}_A$, with tensor factors placed in the stated order. Summing $|y⟩⟨y|\otimes {\hat{\Phi }}_y(X)$ gives the ready record channel. The full channel is its mixture with the reset-failure branch.

No failure is deleted and no surviving branch is renormalized.