Manuscript Oai280-C@1 · Oai280-C.tex · proposition · 7d44b8c0

Proposition: A forty-shot limitation

Feasibility and certificate-specific shot limitations › Why forty shots cannot pass this Hoeffding certificate · lines 1832–1860 · proof included or linked

Oai280-C@1#prop:forty

Back to manuscript

Use Corollary cor:bell with no calibration or transfer allowance. If each of the three settings has at most forty shots and each two-sided allocation satisfies $0 < δ_{i} \leq 1$ , then no data set can certify a threshold $ε = 0.1$ . The statement also covers forty shots in total.

Proof. Each radius satisfies

t_{i} \geq 2 lo g 2/40 .

Since the measured correlations lie in $[- 1, 1]$ , $f \leq 1$ and

1 - f_{L} \geq min {1, \frac{3}{4} 2 lo g 2/40} .

Therefore the best possible upper certificate is at least

min {1, 2 \frac{3}{4} 2 lo g 2/40} > 0.74.

It cannot be at most $0.1$ .

Displayed formulas in this passage

unlabeled · line 1843
$t_{i} \geq 2 lo g 2/40 .$
unlabeled · line 1848
$1 - f_{L} \geq min {1, \frac{3}{4} 2 lo g 2/40} .$
unlabeled · line 1853
$min {1, 2 \frac{3}{4} 2 lo g 2/40} > 0.74.$

Nearby in this section

section: Why forty shots cannot pass this Hoeffding certificate