Data from: Revealing quantum-classical correspondence through weak-value metrology of action in photonic path integrals

The quantum-classical correspondence (QCC) describes how quantum systems recover classical behavior in the semiclassical limit. One of the crucial mechanisms to this correspondence is the concept of action, which governs dynamics in both classical mechanics and quantum path integrals. Despite its fundamental importance, direct experimental access to the action of individual quantum paths has remained elusive. Here, we experimentally propose and experimentally demonstrate a direct method to measure the action of quantum paths between fixed spacetime points, based on weak-value measurement techniques. By introducing and analyzing the spectrum of the norm of the action gradient, we identify not only single but also multiple stationary-action paths in systems exhibiting complex QCC. Using an optical setup that simulates photon propagation in free space and under an impulsive potential, we reconstruct pathwise actions and observe sharp dips in the spectrum that correspond precisely to classical trajectories. This work establishes a general framework for directly accessing the action, opening new avenues for experimentally exploring the QCC. This dataset supports the study "Revealing Quantum-Classical Correspondence through Action Measurement in Photonic Path Integrals". It provides the experimental and processed data that enable full reproduction of the figures in the associated manuscript.