Theory for quantum state of photon pairs generated from spontaneous   parametric down conversion nonlinear process
  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. 
Ruo Peng Wang, Hui Rong Zhang