Quantum non-Gaussianity and quantification of nonclassicality

TL;DR

This paper introduces a method to quantify and certify quantum non-Gaussianity using nonclassicality quasiprobabilities derived from non-Gaussian filtering of the $P$ function, providing new insights into quantum state properties.

Contribution

The authors develop a novel approach to quantify and certify quantum non-Gaussianity directly from experimentally accessible quasiprobabilities, improving upon existing state representations.

Findings

Lower bounds for nonclassicality degree established.

Bounds for convex Gaussian mixtures derived.

Applied method to multi-photon-added squeezed states.

Abstract

The algebraic quantification of nonclassicality, which naturally arises from the quantum superposition principle, is related to properties of regular nonclassicality quasiprobabilities. The latter are obtained by non-Gaussian filtering of the Glauber-Sudarshan $P$~function. They yield lower bounds for the degree of nonclassicality. We also derive bounds for convex combinations of Gaussian states for certifying quantum non-Gaussianity directly from the experimentally accessible nonclassicality quasiprobabilities. Other quantum-state representations, such as $s$-parametrized quasiprobabilities, insufficiently indicate or even fail to directly uncover detailed information on the properties of quantum states. As an example, our approach is applied to multi-photon-added squeezed vacuum states.