Universal Free-Electron-Sideband Control

arXiv:2611.04432v1 Announce Type: new Abstract: Advances in free-electron quantum optics are establishing free electrons as a versatile quantum resource. Photon-induced near-field electron microscopy (PINEM) interactions and free drift provide elementary operations for shaping the longitudinal electron wavefunction, yet their full control capabilities remain unexplored. Here, we prove that a finite sequence of alternating monochromatic PINEM interactions and free drifts can approximate any prescribed inner-product-preserving map from a finite-dimensional input subspace into the full ideal electron-sideband Hilbert space to arbitrary accuracy. We therefore call the protocol PINEMAD (PINEM And Drift). This framework encompasses state preparation, unitary gates, and isometric encoding.