Manuscript Hawk01-B@1 · Hawk01-B.tex · lemma · cfa976f1

Lemma: KSW continuity input

Exact and approximate residual-leakage certificates › The half-diamond normalization audit · lines 378–391

Hawk01-B@1#lem:KSW, Hawk01-B@1#eq:KSWraw

After padding their dilation spaces when necessary, channels $Φ, Ψ$ admit Stinespring isometries with optimized operator-norm distance $β$ satisfying

β^{2} \leq ∥ Φ - Ψ ∥_{⋄} \leq 2 β .

This is Theorem 1 of Kretschmann–Schlingemann–Werner, expressed through the Schrödinger dual of its completely bounded norm.

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