Phase-sensitive classification under dephasing

This supplies a genuine phase-sensitive observable in the newly defined model. The exponential form resembles the independent pilot in Psy02-B; no carrier identification is inferred from that resemblance CheungPsy02A,CheungPsy02B.

For this fixed task, reducing $\gamma$ at fixed $T$ strictly improves success. The exact operational displacement is

Indeed (eq:dephchannel) expresses the difference as a scalar multiple of $\mathrm{id}-{\mathrm{Ad}}_Z$, whose half-diamond norm is one. For $\lambda >{\lambda }^{\prime }$, the success improvement equals this distance.