Quantifying the non-Gaussian character of a quantum state by quantum relative entropy

TL;DR

This paper introduces a new measure based on quantum relative entropy to quantify how non-Gaussian a quantum state is, analyzing its properties and relevance in quantum information processing.

Contribution

It proposes a novel quantum relative entropy measure for non-Gaussianity and explores its properties, relationships with quantum information quantities, and applications in state evolution.

Findings

The measure relates to the Holevo bound and conditional entropy.

Necessary conditions for Gaussian channels are derived.

Non-Gaussianity evolution analyzed during Gaussification and de-Gaussification.

Abstract

We introduce a novel measure to quantify the non-Gaussian character of a quantum state: the quantum relative entropy between the state under examination and a reference Gaussian state. We analyze in details the properties of our measure and illustrate its relationships with relevant quantities in quantum information as the Holevo bound and the conditional entropy; in particular a necessary condition for the Gaussian character of a quantum channel is also derived. The evolution of non-Gaussianity (nonG) is analyzedfor quantum states undergoing conditional Gaussification towards twin-beam and de-Gaussification driven by Kerr interaction. Our analysis allows to assess nonG as a resource for quantum information and, in turn, to evaluate the performances of Gaussification and de-Gaussification protocols.