  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.
