Tomographic reconstruction of free-electron quantum states

We give several algorithms for reconstructing quantum states of swift electrons, using maximum likelihood estimation, Bayesian inversion, and deep learning. We apply these algorithms to data previously recorded for an attosecond electron pulse-train to retrieve the density matrix and to analyse its physical properties. Based on the reconstructed quantum state, we obtain pulse-durations of about 245as and predict a degree of coherence of 36 per cent for radiations and excitations produced by these electrons.