Entanglement engineering plays a central role in quantum-enhanced technologies, with potential physical platforms that outperform their classical counterparts. However, free electrons remain largely unexplored despite their great capacity to encode and manipulate quantum information, due in part the lack of a suitable theoretical framework. Here we link theoretical concepts from quantum information to available free-electron sources. Specifically, we consider the interactions among electrons propagating near the surface of a polariton-supporting medium, and study the entanglement induced by pair-wise coupling. These correlations depend on controlled interaction interval and the initial electron bandwidth. We show that long interaction times of broadband electrons extend their temporal coherence. This in turn is revealed through a widened Hong-Ou-Mandel peak, and associated with an increased entanglement entropy. We then introduce a discrete basis of electronic temporal-modes, and discriminate between them via coincidence detection with a shaped probe. This paves the way for ultrafast quantum information transfer by means of free electrons, rendering the large alphabet that they span in the time domain accessible.
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