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The polarization rotator is then designed with the specific dimensions such that horizontal polarization is switched to vertical polarization. Thus any pairs of photons generated before the rotator exit the waveguide with vertical polarization and any pairs generated on the other end of the wire exit the waveguide still having horizontal polarization. Mathematically, the process is, up to overall normalization,
::<math>|\alpha\rangle\rightarrow|\alpha'\rangle+|H_s,H_i\rangle\rightarrow|\alpha'\rangle+|V_s,V_i\rangle\rightarrow
Assuming that equal space on each side of the rotator makes spontaneous four-wave mixing equally likely one each side, the output state of the photons is maximally entangled:
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