Alternative non-Gaussianity measures for quantum states based on quantum fidelity

doi:10.1088/1674-1056/ac1928

中国物理B ›› 2022, Vol. 31 ›› Issue (3): 30306-030306.doi: 10.1088/1674-1056/ac1928

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

收稿日期:2021-05-13 修回日期:2021-07-23 接受日期:2021-07-30 出版日期:2022-02-22 发布日期:2022-02-14
通讯作者: Shao-Hua Xiang E-mail:shxiang97@163.com
基金资助:
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).

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

Received:2021-05-13 Revised:2021-07-23 Accepted:2021-07-30 Online:2022-02-22 Published:2022-02-14
Contact: Shao-Hua Xiang E-mail:shxiang97@163.com
Supported by:
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).

摘要/Abstract

摘要： 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. A 373 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.

关键词: non-Gaussianity, quantum fidelity, non-Gaussian states, sine metric

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. A 373 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.

Key words: non-Gaussianity, quantum fidelity, non-Gaussian states, sine metric

中图分类号: (Entanglement measures, witnesses, and other characterizations)

03.67.Mn

03.67.-a (Quantum information) 03.65.Ta (Foundations of quantum mechanics; measurement theory)

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[J]. 中国物理B, 2022, 31(3): 30306-030306.

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[J]. Chin. Phys. B, 2022, 31(3): 30306-030306.

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Alternative non-Gaussianity measures for quantum states based on quantum fidelity

Alternative non-Gaussianity measures for quantum states based on quantum fidelity

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