Polarization-controlled Kerr rotation
= Polarization-controlled Kerr rotation
{title2=$U=e^{i\Theta n_1|V\rangle\langle V|}$}
A one-photon polarization qubit can conditionally rotate another mode's coherent amplitude: the horizontal branch leaves $\alpha$ unchanged and the vertical branch gives $\alpha e^{i\Theta}$. The output is generally entangled. Measuring the polarization in a <superposition> basis can erase the branch label and prepare a coherent <superposition> of the two amplitudes.