Postselection probability for Kerr-cat preparation
= Postselection probability for Kerr-cat preparation
{title2=$p_V=(1+e^{-2|\alpha|^2}\cos\phi)/2$}
Normalize the initial polarization qubit and its analysing wave-plate transformation. For a conditional phase rotation of $\pi$, a vertical detection has the displayed probability and prepares $N(|\alpha\rangle+e^{i\phi}|-\alpha\rangle)$. At $\alpha=0,\phi=\pi$, that outcome has zero probability, explaining the singular normalization of the absent branch.