Manuscript Hawk07-B@1 · Hawk07-B.tex · example · b9785538

Example: The threshold is not universally necessary

Payload-resource tradeoffs before a positive cutoff › A sufficient certified payload allowance · lines 776–787

With $U = I$ , release the diary $L$ , retain $H$ , and take $h \geq 2$ . Then

V ∣ ψ ⟩ = ∣ ψ ⟩_{P} ∣ Φ_{h} ⟩_{H E}, R = P E, B = H .

Tracing $E$ is an exact decoder even though $r = d$ . Consequently the $d^{2} ε^{- 2}$ law is not a lower bound on every operational certificate. It is the sufficient scaling established for the Haar estimate.

Displayed formulas in this passage

unlabeled · line 779
$V ∣ ψ ⟩ = ∣ ψ ⟩_{P} ∣ Φ_{h} ⟩_{H E}, R = P E, B = H .$

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section: A sufficient certified payload allowance
section: A sufficient certified payload allowance