photon pairs have trajectories that are constrained along the sides of two cones whose axes are symmetrically arranged relative to the pump beam. Due to the conservation of momentum, the two photons are always symmetrically located on the sides of the cones, relative to the pump beam. In particular, the trajectories of a small proportion of photon pairs will lie simultaneously on the two lines where the surfaces of the two cones intersect. This results in entanglement of the polarizations of the pairs of photons emerging on those two lines. The photon pairs are in an equal weight quantum superposition of the unentangled states and , corresponding to polarizations of left-hand side photon, right-hand side photon. Another crystal is KDP (potassium dihydrogen phosphate) which is mostly used in Type I down conversion, where both photons have the same polarization. Some of the characteristics of effective parametric down-converting nonlinear crystals include: Nonlinearity: The refractive index of the crystal changes with the intensity of the incident light. This is known as the nonlinear optical response. Periodicity: The crystal has a regular, repeating structure. This is known as the lattice structure, which is responsible for the regular arrangement of the atoms in the crystal. Optical anisotropy: The crystal has different refractive indices along different crystallographic axes. Temperature and pressure sensitivity: The nonlinearity of the crystal can change with temperature and pressure, and thus the crystal should be kept in a stable temperature and pressure environment. High nonlinear coefficient: Large nonlinear coefficient is desirable, this allow to generate a high number of entangled photons. High optical damage threshold: Crystal with high optical damage threshold can endure high intensity of the pumping beam. Transparency in the desired wavelength range: It is important for the crystal to be transparent in the wavelength range of the pump beam for efficient nonlinear interactions High optical quality and low absorption: The crystal should be high optical quality and low absorption to minimize loss of the pump beam and the generated entangled photons. History SPDC was demonstrated as early as 1967 by S. E. Harris, M. K. Oshman, and R.L. Byer, as well as by D. Magde and H. Mahr. It was first applied to experiments related to coherence by two independent pairs of researchers in the late 1980s: Carroll Alley and Yanhua Shih, and Rupamanjari Ghosh and Leonard Mandel. The duality between incoherent (Van Cittert–Zernike theorem) and biphoton emissions