Theorem: Radiation and complementary stability

The implemented prefix channels and the complements defined with the same complete environment interface differ from their ideal counterparts by at most ${ϵ}_{\mathrm{dyn}}$.

With the exact decoder,

A fixed Bell-test fidelity changes by at most ${ϵ}_{\mathrm{dyn}}$.

Proof. Encoding, independent preparation, and dynamics telescope by Lemma lem:stability. Either accessible or complementary partial trace is contractive. Decoder postcomposition and the triangle inequality give the recovery bound. The Bell projector is an effect, so its expectation changes by at most trace distance.