= Equatorial measurement relabeling at Clifford angles
{title2=$|v_s(\eta+\pi)\rangle=|v_{s\oplus1}(\eta)\rangle$}
For $|v_s(\eta)\rangle=(|0\rangle+(-1)^s e^{i\eta}|1\rangle)/\sqrt2$, adding $\pi$ exchanges the two outcomes of the same <projective measurement>. At an angle $\phi=j\pi/2$, the choices $\phi$ and $-\phi$ therefore specify the same unordered pair of projectors: their labels differ by $j\bmod2$. An adaptive choice between these signs can be replaced by a fixed measurement and a classical label exchange. Together with <Pauli-frame propagation along a measurement wire>, this permits simultaneous measurements when all adaptive sign changes occur at these <Clifford gate> angles.
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