Polarization entanglement in a crystal with threefold symmetry

Polarization entanglement of twin photons created in the process of parametric down-conversion is fully determined by the pump polarization when the pump, signal, and idler beams are collinear with the symmetry axis of the nonlinear crystal. We point out that in this situation a threefold rotational symmetry is needed for the process to occur. We describe the polarization entanglement of the twin photons in terms of correlations on the Poincare sphere. The inherent nonconservation of the intrinsic angular momentum of light in this process is discussed.