= Solution
One implementation uses <type-II phase matching> for <spontaneous parametric down-conversion> in a nonlinear birefringent crystal pumped by a coherent laser. A pump photon produces two lower-frequency photons of orthogonal <polarizations>, subject to <energy> and momentum <phase> matching. Collect two spatial modes in which the alternatives “horizontal photon in Alice's mode and vertical photon in Bob's mode” and the reversed assignment are indistinguishable. Compensation crystals, filters and matched optical paths erase polarization-dependent timing and spectral information. The <amplitudes> then add coherently to give a state proportional to $|HV\rangle+e^{i\varphi}|VH\rangle$; a birefringent <phase> element tunes $\varphi$.
The essential requirement is coherent indistinguishability of the two assignments. Producing two orthogonally polarized photons with information revealing which assignment occurred would instead give a mixture without the required <polarization> <entanglement>.
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