# Continuous-Variable Tomography of Solitary Electrons

## TL;DR

This paper introduces a wideband quantum tomography method for solitary electrons, enabling detailed characterization of their wave-functions and quantum properties, which advances quantum information processing with single electrons.

## Contribution

It demonstrates a novel energy-time filtering technique for wideband electron tomography and reconstructs the Wigner function of solitary electrons emitted on demand.

## Key findings

- Partial resolution of the Wigner function's chirp and squeezing.
- Quantification of the source’s quantumness despite classical fluctuations.
- Potential for quantum-limited measurements of electron coherence.

## Abstract

A method for characterising the wave-function of freely-propagating particles would provide a useful tool for developing quantum-information technologies with single electronic excitations. Previous continuous-variable quantum tomography techniques developed to analyse electronic excitations in the energy-time domain have been limited to energies close to the Fermi level. We show that a wideband tomography of single-particle distributions is possible using energy-time filtering and that the Wigner representation of the mixed-state density matrix can be reconstructed for solitary electrons emitted by an on-demand single-electron source. These are highly localised distributions, isolated from the Fermi sea. While we cannot resolve the pure state Wigner function of our excitations due to classical fluctuations, we can partially resolve the chirp and squeezing of the Wigner function imposed by emission conditions and quantify the quantumness of the source. This tomography scheme, when implemented with sufficient experimental resolution, will enable quantum-limited measurements, providing information on electron coherence and entanglement at the individual particle level.