State-Agnostic Electron-Photon Pair Entanglement Certification in TEM

Abstract

The integration of quantum correlations into transmission electron microscopy (TEM) offers new possibilities for advanced imaging and hybrid quantum sensing, with potential benefits such as enhanced contrast mechanisms and reduced radiation dose for sensitive samples [1-4]. Recent experiments have demonstrated electron photon entanglement for the first time [1, 2]. However, these demonstrations often rely on specific assumptions about the states. In this work, we present an approach for entanglement certification that does not depend on such assumptions. Specifically, we propose and analyze a robust, state-agnostic protocol for certifying electron photon entanglement using mutually unbiased bases in position and momentum [3, 5]. Our simulations, based on a Cherenkov radiation model, describe the entangling interaction between a fast electron and the electromagnetic field generated by a dielectric medium. Conservation of energy and momentum naturally correlates the electron and the emitted photon [6-8]. We quantify these correlations, establish a lower bound on the entanglement of formation, and demonstrate that certification is feasible under realistic experimental conditions including uncertainties in both position and momentum measurements [1, 3].