Electron quantum optics as quantum signal processing

The recent developments of electron quantum optics in quantum Hall edge channels have given us new ways to probe the behavior of electrons in quantum conductors. It has brought new quantities called electronic coherences under the spotlight. In this paper, we explore the relations between electron quantum optics and signal processing through a global review of the various methods for accessing single- and two-electron coherences in electron quantum optics. We interpret electron quantum optics interference experiments as analog signal processing converting quantum signals into experimentally observable quantities such as current averages and correlations. This point of view also gives us a procedure to obtain quantum information quantities from electron quantum optics coherences. We illustrate these ideas by discussing two mode entanglement in electron quantum optics. We also sketch how signal processing ideas may open new perspectives for representing electronic coherences in quantum conductors and understand the properties of the underlying many-body electronic state.
Comment: 19 pages, 9 figures, to appear in Physical Status Solidi B focus issue on 'Single-electron control in solid-state devices'. Version 2 & 3: expanded section 2 with extra-references reviewing electron quantum optics in other systems and updated bibliography+ corrected misprints + corrected Figs. 8 & 9 and associated comments due to a small error in numerics: no change to conclusions