= Measurement-guided Zeno transfer
{title2=$P_N=\cos^{2N}(\pi/(2N))\to1$}
Successively measure in bases whose first vector rotates from $|0\rangle$ to $|1\rangle$ in $N$ equal angular steps. The probability to remain on that branch throughout is the displayed product of squared overlaps. Without postselection, the final target probability is $[1+\cos^N(\pi/N)]/2$. Both approach one for an initial $|0\rangle$, but a general input loses its relative phase between the two measurement branches; the process does not implement a coherent <Pauli X gate> on unknown inputs.
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