Proposed Experiment to Test Single-Electron Entanglement of Spin and Space

Single-electron entanglement (SEE) is of interest for applications in quantum communication. We consider SEE between the spatially dependent functional space and the spinor space of an electron beam. Following Eberly et al. [Optica 2, 611-615 (2015)], we reformulate the electronic spinor state as a tensor product between the functional and spinor spaces and use the Schmidt decomposition to identify a recognizable entangled state. We then construct a Bell-like test for confirming entanglement of the two spaces. Finally, we propose an experiment to violate the Bell-type inequality and which makes use of recently developed spin-polarizing electron beam splitters [Dellweg and Müller: Phys. Rev. Lett. 118, 070403 (2017)].