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.