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(College of Physics,Electronics and Intelligent Manufacturing,Huaihua University,Huaihua 418008,China;Hunan Provincial Key Laboratory of Ecological Agriculture Intelligent Control Technology,Huaihua 418008,China;Research Center for Information Technological Innovation,Huaihua University,Huaihua 418008,China)

机构地区：[1]College of Physics,Electronics and Intelligent Manufacturing,Huaihua University,Huaihua 418008,China [2]Hunan Provincial Key Laboratory of Ecological Agriculture Intelligent Control Technology,Huaihua 418008,China [3]Research Center for Information Technological Innovation,Huaihua University,Huaihua 418008,China

出　　处：《Chinese Physics B》2023年第5期297-307,共11页中国物理B（英文版）

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)。

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.

关 键 词：non-Gaussianity measure non-Gaussian states phase-space distribution function 

分 类 号：O431.2[机械工程—光学工程]