Projection measurement of the comb basis through free-electron-photon interactions

Free electrons, driven by rapid advances in photon-induced near-field electron microscopy, have emerged as a promising platform for quantum information processing, including quantum computing and quantum sensing. However, conventional measurements that rely on the electron energy loss spectrum (EELS) are inherently destructive to electron qubits, thereby constraining their applicability. In this Letter, we propose a scheme that performs projection measurement on the electron comb basis, where high measurement precision can be achieved with bright squeezed vacuum states and strong PINEM couplings. Notably, this approach is not only nondestructive to electron qubits but also maximally incompatible with energy measurements, enabling alternative quantum information applications, such as quantum error mitigation and Einstein-Podolsky-Rosen steering detection. Our findings open an avenue towards a systematic understanding of quantum free electrons and towards the development of nondestructive free electron quantum information tasks.