  We present a theory for the quantum state of photon pairs generated from
spontaneous parametric down conversion nonlinear process in which the influence
of the final sizes of nonlinear optical crystals on eigen optical modes is
explicitly taken into consideration. We find that these photon pairs are not in
entangled quantum states. Polarization correlations between the signal beam and
the idler beam are explained. We also show that the two photons generated from
SPDC are not spatially separated, therefore the polarization correlation
between the signal and idler beams is not an evidence for quantum non-locality.
