Angular Schmidt spectrum of entangled photons: derivation of an exact formula and experimental characterization for non-collinear phase matching.

We derive an exact formula for the angular Schmidt spectrum of the orbital angular momentum (OAM)-entangled states produced by parametric down-conversion (PDC). We show that our formula yields true theoretical spectrum without any convergence issue as has been the case with the previously derived formulas. Furthermore, we use this formula to experimentally characterize the angular Schmidt spectrum for non-collinear PDC. We report the measurements of very broad angular Schmidt spectra corresponding to angular Schmidt numbers up to 233, which, to the best of our knowledge, is the highest number reported so far. Our studies can be very important for OAM-based quantum information applications.