Faithful measure of Quantum non-Gaussianity via quantum relative entropy

TL;DR

This paper proposes a new quantum non-Gaussianity measure based on quantum relative entropy, which is a proper monotone under Gaussian operations and can be explicitly calculated for noisy single-photon states.

Contribution

It introduces a convex-roof based QNG measure that extends beyond pure states and satisfies key monotonicity properties, advancing the quantification of non-Gaussianity.

Findings

QNG measure is explicitly calculated for noisy single-photon states.

QNG coincides with the state's non-Gaussianity when the single-photon fraction is high.

The measure fulfills desired properties as a proper monotone under Gaussian channels.

Abstract

We introduce a measure of quantum non-Gaussianity (QNG) for those quantum states not accessible by a mixture of Gaussian states in terms of quantum relative entropy. Specifically, we employ a convex-roof extension using all possible mixed-state decompositions beyond the usual pure-state decompositions. We prove that this approach brings a QNG measure fulfilling the properties desired as a proper monotone under Gaussian channels and conditional Gaussian operations. As an illustration, we explicitly calculate QNG for the noisy single-photon states and demonstrate that QNG coincides with non-Gaussianity of the state itself when the single-photon fraction is sufficiently large.