Quantum Interference of Different Photons and Indistinguishability of Probability Amplitudes

This article reviews the historical and conceptual evolution of quantum physics, challenging P.A.M. Dirac’s famous dictum, “Each photon then interferes only with itself. Interference between two different photons never occurs.” We trace the progression from the early experiments by Forrester et al. and Magyar & Mandel, which first questioned this notion, to the advent of Spontaneous Parametric Down-Conversion (SPDC) following the invention of the laser and nonlinear optics. The article elucidates how D. N. Klyshko’s quantum description of SPDC laid the groundwork for the landmark Shih-Alley and Hong-Ou-Mandel (HOM) experiments, which demonstrated two-photon quantum interference and entanglement. Finally, we address the common misconception that photons must physically overlap at a beam splitter for two-photon interference to occur. We illustrate that quantum interference arises solely from the indistinguishability of probability amplitudes leading to a joint detection event, even in configurations where the photons never locally interact at a beam splitter.