Electron quantum optics as signal processing

Electron quantum optics is an emerging field aiming at understanding quantum transport using ideas from photon quantum optics [Annalen der Physik, {\bf 526}, 1 (2014)]. The key question in electron quantum optics is to determine which single-electron and more generally many-electron wavefunctions are propagating in the conductor. This is encoded within the electronic coherences defined similarily to the Glauber correlation function of order $n$ giving access to the result of every $n$-particle interferometry experiments. This raises the question of the best elementary signals describing the electronic coherences of a periodically driven electronic source [arXiv:1610.02086]. In this work, we introduce the spectral decomposition of the electron and hole parts of the first-order coherence. From this, we compute the best elementary signals describing a periodic source. Whenever interactions can be neglected, we can reconstruct the whole many-body state. We then define a many-body notion of entanglement spectrum giving a many-body criterion for pure electron or hole emission relevant when considering a driven Ohmic contact or the mesoscopic capacitor. This work is a first step towards the development of quantum signal processing techniques in electron quantum optics.