Research Progress of the Measurement of Propagators in Path Integrals

The propagator plays a central role in path integral theory and therefore has significant value in various modern quantum physics fields where path integral representations can be used. However, due to the fact that it has not been directly measured in experiments, progress in experimental studies of quantum systems based on path integral representations has been severely limited. Recently, we proposed a propagator measurement scheme based on direct measurement of the wave function and successfully performed the first experimental measurement of the propagator using a single photon experiment. Furthermore, in this study, the quantum principle of least action was demonstrated for the first time. This research successfully addressed the technical challenges of path integral experimental studies. In this article, we will review the research progress in this field, including a brief introduction to the basic concepts and research progress of direct wave function measurement, and a detailed description of the theoretical model, experimental design, and experimental results of propagator measurement. Finally, we will introduce an important application example, which is the experimental demonstration of the quantum principle of least action through propagator measurement. The research progress in propagator measurement reviewed in this article will provide important references for future experimental studies using this method.