Alternative non-Gaussianity measures for quantum states based on quantum fidelity
Cheng Xiang(向成)1,2, Shan-Shan Li(李珊珊)1,2, Sha-Sha Wen(文莎莎)1,2, and Shao-Hua Xiang(向少华)1,2,†
1 College of Electrical and Information Engineering, Huaihua University, Huaihua 418008, China; 2 Hunan Provincial Key Laboratory of Ecological Agriculture Intelligent Control Technology, Huaihua 418008, China
Abstract We propose three alternative measures for non-Gaussianity of quantum states: sine distance, Bures angle, and Bures distance, which are based on quantum fidelity introduced by Wang [Phys. Lett. A373 58 (2008)]. Using them, we evaluate the non-Gaussianity of some relevant single-mode and two-mode non-Gaussian states and find a good consistency of the three examined measures. In addition, we show that such metrics can exactly quantify the degree of Gaussianity of even Schrödinger-cat-like states of small amplitudes that can not be measured by other known non-Gaussianity measures such as the Hilbert—Schmidt metric and the relative entropy metric. We make a comparative study between all existing non-Gaussianity measures according to the metric axioms and point out that the sine distance is the best candidate among them.
(Foundations of quantum mechanics; measurement theory)
Fund: Project supported by the Natural Science Foundation of Hunan Province, China (Grant No. 2021JJ30535), the Science and Technology Innovation Foundation for College Students in Hunan Province of China (Grant No. 2020RC1013), and the Research Foundation for Young Teachers from the Education Department of Hunan Province of China (Grant No. 20B460).
Cheng Xiang(向成), Shan-Shan Li(李珊珊), Sha-Sha Wen(文莎莎), and Shao-Hua Xiang(向少华) Alternative non-Gaussianity measures for quantum states based on quantum fidelity 2022 Chin. Phys. B 31 030306
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