ABSTRACT
This chapter provides the ubiquitous equation for the probability amplitude of polarization entanglement of two photons moving away in different directions, from a common source. The first derivation is performed from a Hamiltonian approach using the two-state infrastructure taught to by R. P. Feynman. The second derivation utilizes an interferometric approach, while the third approach is based on the original analysis used by Ward. The initial link between quantum mechanical concepts and the polarization correlation of photons propagating in opposite directions was given by Wheeler: “According to the pair theory, if one of these photons is polarized in one plane, then the photon that goes off in the opposite direction with equal momentum is linearly polarized in the perpendicular plane.” The theory of entangled quantum polarizations, central to A. Einstein, B. Podolsky, and N. Rosen-type optical experiments, was established in the 1947–1949 period by M. H. Pryce and J. C. Ward and independently by H. S. Snyder et al.
