Abstract

We analyze a completely specified even-parity excitation-qubit extraction channel and its full complementary channel. The signed isometry yields exact formulas for transferred occupation, occupation-basis coherence, subsystem purity, reference correlations, and deterministic recovery performance. For a Bell input, we determine the accessible and residual spectra, their mutual-information balance, and the reference–accessible negativity. A complete specified decoder has half-diamond error $1-\eta$, Bell fidelity $(1+3\eta )/4$, worst-case target overlap $\eta$, and decoded reference concurrence $\eta$. We distinguish these formulas from optimal recovery and determine the optimal errors at zero and full transfer.

An independently declared population-preserving output dephasing experiment retains its additional environment. At full transfer, its optimal recovery error is $(1-\lambda )/2$, while the Bell-input accessible marginal, occupation, and purity are independent of $\lambda$. Complete dephasing therefore leaves perfect occupation delivery and an unchanged accessible marginal, but destroys reference entanglement and prevents exact quantum recovery. These results provide a self-contained information-flow benchmark. They neither identify the channel with black-hole evaporation nor establish a gravitational Page curve. No numerical execution or completed verification package is asserted.