Efficient detection of non-Gaussian states via Wigner-function test
Phys. Rev. A 113, 043721 – Published 13 April, 2026
DOI: https://doi.org/10.1103/sp7n-q2s1
Abstract
In continuous-variable quantum information, nonclassicality and non-Gaussianity serve as valuable resources for achieving quantum advantages in various quantum information processing tasks. For a judicious use of non-Gaussian resources, identifying and characterizing non-Gaussianity is a crucial prerequisite. In this work, we develop efficient criteria for detecting non-Gaussianity and quantum non-Gaussianity of single-mode non-Gaussian states, the latter being a stricter nonclassical notion of non-Gaussianity, by probing only a few points in phase space. Our approach draws on the observation that the fluctuation of the Wigner function profile is relatively constrained for the case of Gaussian states. Our criteria are thus effective for identifying non-Gaussian states whose Wigner functions have sharp changes or peaks. We demonstrate the detection of non-Gaussianity as well as quantum non-Gaussianity through prototypical examples such as mixtures of Fock states and Gottesman-Kitaev-Preskill states.
