Certification of non-Gaussian states with operational measurements

TL;DR

This paper develops a practical method using double homodyne detection to certify non-Gaussian features of quantum states, including Wigner negativity, and introduces a hierarchy for ranking these states.

Contribution

It introduces a theoretical framework and practical witnesses for certifying non-Gaussian quantum states with double homodyne detection, extending the stellar hierarchy.

Findings

Effective Wigner negativity witnesses proposed

Simulation results demonstrate certification capabilities

Robustness of the stellar hierarchy confirmed

Abstract

We derive a theoretical framework for the experimental certification of non-Gaussian features of quantum states using double homodyne detection. We rank experimental non-Gaussian states according to the recently defined stellar hierarchy and we propose practical Wigner negativity witnesses. We simulate various use-cases ranging from fidelity estimation to witnessing Wigner negativity. Moreover, we extend results on the robustness of the stellar hierarchy of non-Gaussian states. Our results illustrate the usefulness of double homodyne detection as a practical measurement scheme for retrieving information about continuous variable quantum states.