Outcome mixing can destroy coherence

Without the phase bound, two equal-amplitude outcome blocks with phases zero and $\pi$ can cancel completely. Keeping $z$ avoids this particular loss of phase information.

For a Gaussian preparation and a window whose peak separation lies within ${\delta }_d$ of $\bar{d}$,

Combining this bound, Proposition prop:width, and Proposition prop:window supplies a preparation residual for a nominal attenuation contrast. It does not justify replacing that preparation by one free common offset.