Stability and dimension-explicit conversion

These stability statements agree with the supplied Hawk02-A interface and Hawk04-A/B proofs CheungHawk02A,CheungHawk04A, CheungHawk04B.

external approximate input. For finite-dimensional complementary channels, the KSW information–disturbance theorem gives

Indeed the full-norm inequality

becomes (eq:KSW) under the half normalization KSW (Theorem 3). We use this approximate theorem only on finite channels. No infinite-output attainment assumption is needed for the proxy lift.