Coherence analysis of local randomness and nonlocal correlation through polarization-basis projections of entangled photon pairs

Polarization-entangled photon pairs generated from second-order nonlinear optical media have been extensively studied for both fundamental research and potential applications of quantum information. In a spontaneous parametric down-conversion process, quantum entanglement between paired photons, often regarded as 'mysterious,' has been demonstrated for local randomness and nonlocal correlation through polarization-basis projections using linear optics (Phys. Rev. A 60, R773 (1999)). Unlike the conventional particle nature-based perspective, this paper presents a coherence analysis rooted in the wave nature of quantum mechanics to examine these well-established quantum phenomena, incorporating polarization control of the paired photons and their projection measurements. First, we analyze the quantum superposition of photon pairs generated randomly from cross-sandwiched nonlinear media, focusing on local randomness, which depends on the incoherence among measured events. Second, we investigate coincidence detection between paired photons to understand the nonlocal correlation arising from independently controlled remote parameters, resulting in an inseparable product-basis relationship. This coherence-based approach sheds light on a deterministic perspective on quantum features, emphasizing the significance of phase information intrinsic to the wave nature of photons, which is incompatible with the particle nature.