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Chin. Phys. B, 2019, Vol. 28(8): 084206    DOI: 10.1088/1674-1056/28/8/084206
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

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
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.
Keywords:  Weyl expansion      Wigner operator      similar transformation      two-mode squeezed state      integration within ordered product (IWOP) technique  
Received:  25 March 2019      Revised:  27 April 2019      Published:  05 August 2019
PACS:  42.50.-p (Quantum optics)  
  03.65.-w (Quantum mechanics)  
Fund: 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).
Corresponding Authors:  Li-Yun Hu, Zhi-Ming Rao     E-mail:  hlyun@jxnu.edu.cn;raozm24@jxnu.edu.cn

Cite this article: 

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 2019 Chin. Phys. B 28 084206

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