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

doi:10.1088/1674-1056/acb0bd

中国物理B ›› 2023, Vol. 32 ›› Issue (5): 50309-050309.doi: 10.1088/1674-1056/acb0bd

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

收稿日期:2022-10-18 修回日期:2022-10-18 接受日期:2023-01-06 出版日期:2023-04-21 发布日期:2023-04-28
通讯作者: Shaohua Xiang E-mail:shxiang97@163.com
基金资助:
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).

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

Received:2022-10-18 Revised:2022-10-18 Accepted:2023-01-06 Online:2023-04-21 Published:2023-04-28
Contact: Shaohua Xiang E-mail:shxiang97@163.com
Supported by:
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).

摘要/Abstract

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 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. 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

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. 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 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. A 86 030102(R) (2012)) and establish a conservation relation of non-Gaussianity and Gaussianity of a quantum state.

Key words: non-Gaussianity measure, non-Gaussian states, phase-space distribution function

中图分类号: (Quantum information)

03.67.-a

03.65.Ta (Foundations of quantum mechanics; measurement theory) 42.50.Dv (Quantum state engineering and measurements)

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[J]. 中国物理B, 2023, 32(5): 50309-050309.

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

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

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