Quantifying non-Gaussianity of quantum-state correlation

TL;DR

This paper investigates how to quantify non-Gaussian quantum correlations, revealing limitations of intuitive measures and proposing a new approach using averaged states to define valid non-Gaussianity measures.

Contribution

It introduces a novel method for measuring non-Gaussian quantum correlations that overcomes previous issues with negativity and monotonicity.

Findings

Intuitive subtraction approach fails to produce non-negative measures.

Averaged states enable valid non-Gaussian correlation measures.

Fidelity-based measure includes computable lower bounds.

Abstract

We consider how to quantify non-Gaussianity for the correlation of a bipartite quantum state by using various measures such as relative entropy and geometric distances. We first show that an intuitive approach, i.e., subtracting the correlation of a reference Gaussian state from that of a target non-Gaussian state, fails to yield a non-negative measure with monotonicity under local Gaussian channels. Our finding clearly manifests that quantum-state correlations generally have no Gaussian extremality. We therefore propose a different approach by introducing relevantly averaged states to address correlation. This enables us to define a non-Gaussianity measure based on, e.g., the trace-distance and the fidelity, fulfilling all requirements as a measure of non-Gaussian correlation. For the case of the fidelity-based measure, we also present readily computable lower bounds of non-Gaussian correlation.