Discarded probability is not a generic coherent error

Flagging the $|1⟩$ component of $|+⟩=(|0⟩+|1⟩)/\sqrt{2}$ produces

In the common three-dimensional space, its trace distance from $|+⟩⟨+|$ is

The removed coherence prevents equality with discarded probability.

En02-E's exact cutoff equality uses its commuting Gaussian-state hypothesis CheungEn02E ({thm:cutoff}). It is not imported here. Em03-F's filtered-test packet bridge is likewise not a complete-channel embedding CheungEm03F ({thm:packetbridge}). Equation (eq:packetcomplete) is proved from the actual identified isometries.

For recovery, packet loss is already included exactly in (eq:packeterrors); its square-root complete comparison allowance is not added again to that ideal term.