The imported approximate conversion

We use the finite-dimensional KSW information–disturbance theorem KSW (Theorem 3). In Schrödinger-picture full-diamond normalization, its recovery direction gives, for any replacement state $\sigma$, a CPTP decoder satisfying

Taking infima and converting to the present convention gives

Only finite complementary channels are used in this approximate step. The theorem supplies a channel conversion, not an estimate of interacting dynamics or an executable receiver.