  We study Higgs diphoton decays, in which both photons undergo nuclear
conversion to electron- positron pairs. The kinematic distribution of the two
electron-positron pairs may be used to probe the CP violating (CPV) coupling of
the Higgs to photons, that may be produced by new physics. Detecting CPV in
this manner requires interference between the spin-polarized helicity
amplitudes for both conversions. We derive leading order, analytic forms for
these amplitudes. In turn, we obtain compact, leading-order expressions for the
full process rate. While performing experiments involving photon conversions
may be challenging, we use the results of our analysis to construct
experimental cuts on certain observables that may enhance sensitivity to CPV.
We show that there exist regions of phase space on which sensitivity to CPV is
of order unity. The statistical sensitivity of these cuts are verified
numerically, using dedicated Monte-Carlo simulations.
