Regular Article

A method for efficiently estimating non-Gaussianity of continuous-variable quantum states

¹ College of Electrical and Information Engineering, Huaihua University, Huaihua 418008, P.R. China
² College of Mechanical, Optoelectronics and Physics, Huaihua University, Huaihua 418008, P.R. China

^a e-mail: shxiang97@163.com

Received: 27 August 2019
Received in final form: 10 November 2019
Published online: 28 January 2020

Abstract

We develop a method for efficiently calculating non-Gaussianity of quantum states in Wigner function representation based on the sine metric. In contradistinction to the known non-Gaussianity measures, we seek the corresponding reference Gaussian counterpart via the cumulant-expansion techniques of quantum state. We analyze this quantity for some non-Gaussian quantum states, which can not be well detected or quantified by other non-Gaussianity measures such as the degree of Gaussianity, the Hilbert-Schmidt metric and the relative entropy metric, thereby providing a good measure to quantify a genuine non-Gaussian state.