Quantifying non-Gaussianity of a quantum state by the negative entropy of quadrature distributions

TL;DR

This paper introduces a new non-Gaussianity measure for multimode quantum states based on negentropy of quadrature distributions, which is experimentally accessible and theoretically well-founded.

Contribution

It proposes a novel non-Gaussianity measure satisfying key properties and relates it quantitatively to existing measures, enabling easier experimental estimation.

Findings

The measure is faithful and invariant under Gaussian unitaries.

It is monotonic under Gaussian channels.

The measure can be estimated via homodyne detection.

Abstract

We propose a non-Gaussianity measure of a multimode quantum state based on the negentropy of quadrature distributions. Our measure satisfies desirable properties as a non-Gaussianity measure, i.e., faithfulness, invariance under Gaussian unitary operations, and monotonicity under Gaussian channels. Furthermore, we find a quantitative relation between our measure and the previously proposed non-Gaussianity measures defined via quantum relative entropy and the quantum Hilbert-Schmidt distance. This allows us to estimate the non-Gaussianity measures readily by homodyne detection, which would otherwise require a full quantum-state tomography.