# A measure of the non-Gaussian character of a quantum state

## TL;DR

This paper introduces a Hilbert-Schmidt distance-based measure to quantify the non-Gaussian character of bosonic quantum states, analyzing its properties and evolution under various processes.

## Contribution

It proposes a new, easily computable non-Gaussianity measure for bosonic quantum states and extends it to quantum operations, enhancing quantification methods.

## Key findings

- The measure effectively quantifies non-Gaussianity in single- and multi-mode states.
- It tracks non-Gaussianity evolution during Gaussification and de-Gaussification processes.
- The measure is computationally straightforward for bosonic systems.

## Abstract

We address the issue of quantifying the non-Gaussian character of a bosonic quantum state and introduce a non-Gaussianity measure based on the Hilbert-Schmidt distance between the state under examination and a reference Gaussian state. We analyze in details the properties of the proposed measure and exploit it to evaluate the non-Gaussianity of some relevant single- and multi-mode quantum states. The evolution of non-Gaussianity is also analyzed for quantum states undergoing the processes of Gaussification by loss and de-Gaussification by photon-subtraction. The suggested measure is easily computable for any state of a bosonic system and allows to define a corresponding measure for the non-Gaussian character of a quantum operation.