# 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.

## Key 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.