Measures of non-Gaussianity for one-mode field states

TL;DR

This paper introduces a new quantum fidelity-based measure of non-Gaussianity for one-mode field states, providing analytical formulas and comparing it with existing measures for specific quantum states.

Contribution

The paper proposes a novel non-Gaussianity measure based on quantum fidelity, applicable to pure and certain mixed states, and compares it with existing measures for thermal states.

Findings

The new measure can be evaluated for all pure states and Fock-diagonal mixed states.

Analytic formulas are derived for specific non-Gaussian states.

The new measure shows good consistency with existing non-Gaussianity measures.

Abstract

We introduce and investigate a distance-type measure of non-Gaussianity based on the quantum fidelity. This new measure can readily be evaluated for all pure states and mixed states that are diagonal in the Fock basis. In particular, for an $M$-photon added thermal state, an analysis of the Bures degree of non-Gaussianity is made in comparison with two previous measures built with the Hilbert-Schmidt metric and the relative entropy. We obtain a compact analytic formula for the Hilbert-Schmidt non-Gaussianity measure and find a good consistency of the three examined measures.