Developing improved measures of non-Gaussianity and Gaussianity for quantum states based on normalized Hilbert–Schmidt distance

作     者：向少华 李珊珊 米贤武 Shaohua Xiang;Shanshan Li;Xianwu Mi

作者机构：College of PhysicsElectronics and Intelligent ManufacturingHuaihua UniversityHuaihua 418008China Hunan Provincial Key Laboratory of Ecological Agriculture Intelligent Control TechnologyHuaihua 418008China Research Center for Information Technological InnovationHuaihua UniversityHuaihua 418008China 

出 版 物：《Chinese Physics B》 (中国物理B（英文版）)

年 卷 期：2023年第32卷第5期

页      面：297-307页

核心收录：

学科分类：070207[理学-光学] 07[理学] 08[工学] 0803[工学-光学工程] 0702[理学-物理学] 

基　　金：the Natural Science Foundation of Hunan Province of China (Grant No. 2021JJ30535) the Research Foundation for Young Teachers from the Education Department of Hunan Province of China (Grant No. 20B460) 

主　　题：non-Gaussianity measure non-Gaussian states phase-space distribution function 

摘      要：Non-Gaussianity of quantum states is a very important source for quantum information technology and can be quantified by using the known squared Hilbert–Schmidt distance recently introduced by Genoni et al.(Phys. Rev. A 78 042327(2007)). It is, however, shown that such a measure has many imperfects such as the lack of the swapping symmetry and the ineffectiveness evaluation of even Schr?dinger-cat-like states with small amplitudes. To deal with these difficulties, we propose an improved measure of non-Gaussianity for quantum states and discuss its properties in detail. We then exploit this improved measure to evaluate the non-Gaussianities of some relevant single-mode non-Gaussian states and multi-mode non-Gaussian entangled states. These results show that our measure is reliable. We also introduce a modified measure for Gaussianity following Mandilara and Cerf(Phys. Rev. A 86 030102(R)(2012)) and establish a conservation relation of non-Gaussianity and Gaussianity of a quantum state.