Evolution of quantum states via Weyl expansion in dissipative channel

doi:10.1088/1674-1056/28/8/084206

中国物理B ›› 2019, Vol. 28 ›› Issue (8): 84206-084206.doi: 10.1088/1674-1056/28/8/084206

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Evolution of quantum states via Weyl expansion in dissipative channel

Li-Yun Hu(胡利云), Zhi-Ming Rao(饶志明), Qing-Qiang Kuang(况庆强)

1 Center for Quantum Science and Technology, Jiangxi Normal University, Nanchang 330022, China;
2 Key Laboratory of Optoelectronic and Telecommunication, Jiangxi Normal University, Nanchang 330022, China

收稿日期:2019-03-25 修回日期:2019-04-27 出版日期:2019-08-05 发布日期:2019-08-05
通讯作者: Li-Yun Hu, Zhi-Ming Rao E-mail:hlyun@jxnu.edu.cn;raozm24@jxnu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11664017), the Outstanding Young Talent Program of Jiangxi Province, China (Grant No. 20171BCB23034), the Degree and Postgraduate Education Teaching Reform Project of Jiangxi Province, China (Grant No. JXYJG-2013-027), and the Science Fund of the Education Department of Jiangxi Province, China (Grant No. GJJ170184).

Evolution of quantum states via Weyl expansion in dissipative channel

Li-Yun Hu(胡利云)^1,2, Zhi-Ming Rao(饶志明)^1,2, Qing-Qiang Kuang(况庆强)²

1 Center for Quantum Science and Technology, Jiangxi Normal University, Nanchang 330022, China;
2 Key Laboratory of Optoelectronic and Telecommunication, Jiangxi Normal University, Nanchang 330022, China

Received:2019-03-25 Revised:2019-04-27 Online:2019-08-05 Published:2019-08-05
Contact: Li-Yun Hu, Zhi-Ming Rao E-mail:hlyun@jxnu.edu.cn;raozm24@jxnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11664017), the Outstanding Young Talent Program of Jiangxi Province, China (Grant No. 20171BCB23034), the Degree and Postgraduate Education Teaching Reform Project of Jiangxi Province, China (Grant No. JXYJG-2013-027), and the Science Fund of the Education Department of Jiangxi Province, China (Grant No. GJJ170184).

摘要/Abstract

摘要： Based on the Weyl expansion representation of Wigner operator and its invariant property under similar transformation, we derived the relationship between input state and output state after a unitary transformation including Wigner function and density operator. It is shown that they can be related by a transformation matrix corresponding to the unitary evolution. In addition, for any density operator going through a dissipative channel, the evolution formula of the Wigner function is also derived. As applications, we considered further the two-mode squeezed vacuum as inputs, and obtained the resulted Wigner function and density operator within normal ordering form. Our method is clear and concise, and can be easily extended to deal with other problems involved in quantum metrology, steering, and quantum information with continuous variable.

关键词: Weyl expansion, Wigner operator, similar transformation, two-mode squeezed state, integration within ordered product (IWOP) technique

Abstract: Based on the Weyl expansion representation of Wigner operator and its invariant property under similar transformation, we derived the relationship between input state and output state after a unitary transformation including Wigner function and density operator. It is shown that they can be related by a transformation matrix corresponding to the unitary evolution. In addition, for any density operator going through a dissipative channel, the evolution formula of the Wigner function is also derived. As applications, we considered further the two-mode squeezed vacuum as inputs, and obtained the resulted Wigner function and density operator within normal ordering form. Our method is clear and concise, and can be easily extended to deal with other problems involved in quantum metrology, steering, and quantum information with continuous variable.

Key words: Weyl expansion, Wigner operator, similar transformation, two-mode squeezed state, integration within ordered product (IWOP) technique

中图分类号: (Quantum optics)

42.50.-p

03.65.-w (Quantum mechanics)

胡利云, 饶志明, 况庆强. Evolution of quantum states via Weyl expansion in dissipative channel[J]. 中国物理B, 2019, 28(8): 84206-084206.

Li-Yun Hu(胡利云), Zhi-Ming Rao(饶志明), Qing-Qiang Kuang(况庆强). Evolution of quantum states via Weyl expansion in dissipative channel[J]. Chin. Phys. B, 2019, 28(8): 84206-084206.

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Evolution of quantum states via Weyl expansion in dissipative channel

Evolution of quantum states via Weyl expansion in dissipative channel

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