Direct experimental test of Feynman's path integral postulates with single photons.

The experimental validation of fundamental thought experiments in quantum mechanics has profoundly advanced quantum science and technology while deepening our understanding of quantum mechanics. However, experimental studies of the path integral formulation, a cornerstone of quantum physics, remain scarce, especially regarding the two fundamental postulates proposed by Feynman in 1948, neither of which has been directly tested. Here, we present a theoretical proposal for the direct experimental test of Feynman's postulates, achieved through the development of a rigorous propagator-based approach. Furthermore, we perform comprehensive measurements of single photon's probability amplitudes for more than 1.4 million (175) paths, achieving high fidelity in propagator measurements and enabling complete reconstruction of the path probability amplitudes. The results confirm both postulates: (i) that quantum probabilities emerge from the coherent superposition of all possible paths and (ii) that all possible paths have equal-magnitude amplitudes, whereas each path's phase is determined by the classical action (in units of ħ). This work not only resolves a longstanding foundational gap but also establishes a general experimental framework for investigating path integrals in contemporary quantum systems.