Developing improved measures of non-Gaussianity and Gaussianity for quantum states based on normalized Hilbert-Schmidt distance
Shaohua Xiang(向少华)1,2,3,†, Shanshan Li(李珊珊)1,2,3, and Xianwu Mi(米贤武)1,2
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
Abstract 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. A78 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 Schrödinger-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. A86 030102(R) (2012)) and establish a conservation relation of non-Gaussianity and Gaussianity of a quantum state.
Fund: Project supported by the Natural Science Foundation of Hunan Province of China (Grant No. 2021JJ30535) and the Research Foundation for Young Teachers from the Education Department of Hunan Province of China (Grant No. 20B460).
Shaohua Xiang(向少华), Shanshan Li(李珊珊), and Xianwu Mi(米贤武) Developing improved measures of non-Gaussianity and Gaussianity for quantum states based on normalized Hilbert-Schmidt distance 2023 Chin. Phys. B 32 050309
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