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Let $\varphi =j\pi /2$ for an integer $j$, and put $q=j\mathrm{mod}2$. Use the fixed phase-measurement angles $(\theta ,0,-\varphi )$ and a fixed final computational basis measurement. Denote their outcomes by $k,l,m,s$. The adaptive construction would instead use $-\varphi$ when $l=0$ and $+\varphi$ when $l=1$.

For the printed measurement vectors,Therefore $+\varphi$ and $-\varphi$ define the same unordered pair of rank-one linear projections; the labels are exchanged if and only if $q=1$. In the branch $l=1$, the outcome that would be called $m_{\mathrm{ad}}$ in the adaptive experiment is thus $m\oplus q$. In both branches,The output correction from the preceding part becomesIf $j$ is even this reduces to $s\oplus k\oplus m$; if $j$ is odd an additional $l$ is included. This equatorial measurement relabeling at Clifford angles changes only the classical interpretation, not any physical measurement basis.

All four fixed single-qubit projective measurements act on different vertices, so their operators commute. They can be performed simultaneously, with the displayed classical correction applied afterward. The first angle $\theta$ may be arbitrary: it was never adaptive. Only the sign choice for the third angle needed to be replaced. Thus the simulation is nonadaptive for every $\varphi \in (\pi /2)\mathbb{Z}$.