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.
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.
作者
Li-Yun Hu
Zhi-Ming Rao
Qing-Qiang Kuang
胡利云;饶志明;况庆强(Center for Quantum Science and Technology,Jiangxi Normal University,Nanchang 330022,China;Key Laboratory of Optoelectronic and Telecommunication,Jiangxi Normal University,Nanchang 330022,China)
基金
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)
the Science Fund of the Education Department of Jiangxi Province,China(Grant No.GJJ170184)
