Corollary: An inhabited finite acceptance example

For the exact one-qubit phase pilot with ideal preparation and tests, let $d=2$, $D=4$, and

The procedure using $15N$ attempted circuit runs certifies the half-diamond threshold $1/4$ with probability at least $1-\alpha$.

Proof. Here $b=0$, and the stated budget gives $e\le 1/32$. On the simultaneous concentration event, the true Choi state equals ${\omega }_U$, so $a\le De/2$. The upper bound in (eq:confidence) is at most $dDe=8e\le 1/4$.