Manuscript Oai272-A@1 · Oai272-A.tex · lemma · a40828a0

Lemma: Represented inputs supply the certificate

The uniform gap and its exact finite certificate › A certificate stated independently of a state construction · lines 806–822 · proof included or linked

Oai272-A@1#lem:Ccertificate

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For $R \in C$ , every completed bit protocol of Specification spec:protocol, with Eve's canonical purification, satisfies Definition def:TC.

Proof. Use Theorem thm:transcript. The fidelity identities give

f (τ_{00} (t), τ_{11} (t)) = ∥ D_{00} (t) R D_{11} (t) ∥_{1} .

Apply Lemma lem:four pointwise and scalar Cauchy–Schwarz to each integral.

Displayed formulas in this passage

unlabeled · line 815
$f (τ_{00} (t), τ_{11} (t)) = ∥ D_{00} (t) R D_{11} (t) ∥_{1} .$

Nearby in this section

definition: Definition: Transcript-coherence certificate
section: A certificate stated independently of a state construction
definition: Definition: Ideal key and distance
section: A certificate stated independently of a state construction
theorem: Theorem: Uniform secret-bit obstruction
section: A certificate stated independently of a state construction