What is the mathematical representation of the operation that type I spontaneous parametric down conversion (SPDC) performs on the polarization of photons, with a photon being represented by [;\lvert\psi\rangle = \alpha\lvert 0\rangle + \beta\lvert 1\rangle;] (i.e., the standard representation of a qubit in a quantum computer)? Would the representation be dependent on the dimensions of the BBO crystal(s) used?
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