Manuscript Hawk04-D@1 · Hawk04-D-v1.tex · lemma · 39b16f67

Lemma: A residual-response witness

Stage 4: information flow, entropy tests, and Page-time limits › The two directions of approximate constancy · lines 1629–1644 · proof included or linked

Hawk04-D@1#lem:response

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If $x = d_{tr} (E (ρ_{0}), E (ρ_{1}))$ , then $δ_{full} (E) \geq x /2$ .

Proof. For every replacement state $σ$ , the triangle inequality gives

x \leq d_{tr} (E (ρ_{0}), σ) + d_{tr} (σ, E (ρ_{1})) \leq 2 d_{⋄} (E, T_{σ}) .

Take the infimum.

Displayed formulas in this passage

unlabeled · line 1638
$x \leq d_{tr} (E (ρ_{0}), σ) + d_{tr} (σ, E (ρ_{1})) \leq 2 d_{⋄} (E, T_{σ}) .$

Nearby in this section

proposition: Proposition: Featureless accessible output is a lower certificate
section: The two directions of approximate constancy