Observation of quantum entanglement between free electrons and photons

Quantum entanglement is central to both the foundations of quantum mechanics and the development of new technologies in information processing, communication, and sensing. Entanglement has been realised in a variety of physical systems, spanning atoms, ions, photons, collective excitations, and hybrid combinations of particles. Remarkably, however, photons and free electrons -- the quanta of light and their most elementary sources -- have never been observed in an entangled state. Here, we demonstrate quantum entanglement between free electrons and photons. We show that entanglement is produced when an electron, prepared in a superposition of two beams, passes a nanostructure and generates transition radiation in a polarisation state tied to the electron path. By implementing quantum state tomography, we reconstruct the full density matrix of the electron-photon pair, and show that the Peres-Horodecki separability criterion is violated by more than 7 standard deviations. Based on this foundational element of emerging free-electron quantum optics, we anticipate manifold developments in enhanced electron imaging and spectroscopy beyond the standard quantum limit. More broadly, the ability to generate and measure entanglement opens electron microscopy to previously inaccessible quantum observables and correlations in solids and nanostructures.