  The fundamental interaction between free electrons and light stands at the
base of both classical and quantum physics, with applications in free-electron
acceleration, radiation sources, and electron microscopy. Yet, to this day, all
experiments involving free-electron light interactions are fully explained by
describing the light as a classical wave, disregarding its quantum nature.
Here, we observe quantum statistics effects of photons on free-electron-light
interactions. We demonstrate interactions passing continuously from Poissonian
to super-Poissonian and up to thermal statistics, unveiling a surprising
manifestation of Bohr's Correspondence Principle: the transition from quantum
walk to classical random walk on the free-electron energy ladder. The electron
walker serves as the probe in non-destructive quantum detection, measuring the
photon-correlation ${g^{(2)} (0)}$ and higher-orders ${g^{(n)} (0)}$. Unlike
conventional quantum-optical detectors, the electron can perform both quantum
weak measurements and projective measurements by evolving into an entangled
joint-state with the photons. Our findings suggest free-electron-based
non-destructive quantum tomography of light, and constitute an important step
towards combined attosecond-temporal and sub-A-spatial resolution microscopy.
