Manuscript Oai280-B@1 · Oai280-B.tex · section · 6d92ab75

Independently established Pauli structure

Feasibility, binomial inversion, and channel structure › Independently established Pauli structure · lines 1727–1752

If Pauli structure is independently valid for every tested $Λ_{0, A}$ , use

L_{A}^{P} = max {0, 1 - F_{U, A} - b_{A}}, U_{A}^{P} = min {1, 1 - F_{L, A} + b_{A}} .

The same coverage theorem follows from Lemma lem:pauli.

With zero allowances and best-case scores, the corresponding requirements are:

n \geq \frac{9}{8 ε ^{2}} lo g \frac{6 K}{α _{s}} for the printed Hoeffding procedure,

and

n \geq \frac{lo g ( 3 K / α _{s} )}{- lo g ( 1 - 2 ε /3 )} for zero-failure acceptance-only binomial inversion .

The latter scales as $\frac{3}{2 ε} lo g (3 K / α_{s})$ .

Displayed formulas in this passage

unlabeled · line 1731
$L_{A}^{P} = max {0, 1 - F_{U, A} - b_{A}}, U_{A}^{P} = min {1, 1 - F_{L, A} + b_{A}} .$
unlabeled · line 1739
$n \geq \frac{9}{8 ε ^{2}} lo g \frac{6 K}{α _{s}} for the printed Hoeffding procedure,$
unlabeled · line 1744
$n \geq \frac{lo g ( 3 K / α _{s} )}{- lo g ( 1 - 2 ε /3 )} for zero-failure acceptance-only binomial inversion .$