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

Abstract: 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 spontaneous parametric down-conversion (SPDC), 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)). This paper presents a coherence analysis of these established quantum phenomena with 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.