New Three-Mode Squeezing Operators Gained via Tripartite Entangled State Representation

We show that the Agarwal-Simon representation of single-mode squeezed states can be generalized to find new form of three-mode squeezed states. We use the tripartite entangled state representations ｜p, y, z） and ｜x, u, v） to realize this goal.

Multipartite State Representations in Multi-mode Fock Space and Their Squeezing Transformations

We present the continuous state vector of the total coordinate of multi-partlcle and the state vector of their total momentum, respectively, which possess completeness relation in multi-mode Fock space by virtue of the integration within an order product （IWOP） technique. We also calculate the transition from classical transformation of variables in the states to quantum unitary operator, deduce a new multi-mode squeezing operator, and discuss its squeezing effect. In progress, it indicates that the IWOP technique provides a convenient way to construct new representation in quantum mechanics.

A generalized Collins formula derived by virtue of the displacement-squeezing related squeezed coherent state representation

Based on the displacement-squeezing related squeezed coherent state representation ｜z〉g and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator, whose matrix element in the coordinate representation leads to a generalized Collins formula （Huygens-Fresnel integration transformation describing optical diffraction）. The generalized Fresnel operator is derived by a quantum mechanical mapping from z to sz -- rz^＊ in the ｜Z〉g representation, while ｜z〉g in phase space is graphically denoted by an ellipse.

The squeezing entangled state of two particles with unequal mass

For two unequal-mass particles,we construct the entangled state representation and then derive the corresponding squeezing operator.This squeezing operator has a natural realization in the entangled state representation,which exhibits the intrinsic relation between squeezing and quantum entanglement.This squeezing operator involves both two-mode squeezing and the direct product of two single-mode squeezings.The maximum squeezing occurs when the two particles possess equal mass.When the two particles＇ mass difference becomes large,the component of the two single-mode squeezings becomes dominant.

Husimi Functions of Excited Squeezed Vacuum States

Based on the Husimi operator in pure state form introduced by Fan et al,which is a squeezed coherentstate projector,and the technique of integration within an ordered product (IWOP) of operators,as well as the entangledstate representations,we obtain the Husimi functions of the excited squeezed vacuum states (ESVS) and two marginaldistributions of the Husimi functions of the ESVS.

Evolution of quantum states via Weyl expansion in dissipative channel

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.

新纠缠态表象的构建及其性质

运用有序算符内积分(IWOP)技术,构建了^x2-^p1和^x1-^p2的共同本征态|η〉,并分析了该新纠缠表象的Schmidt分解形式。另外,我们还得到纠缠态|η〉的共轭态|ξ〉,同时计算了它们的内积。最后我们给出了新双模压缩算符S2=μ∫dπ2η|μη〉〈η|的显式,并分析了其压缩特性。

New generalized bipartite coherent-entangled state representation and its application

The new generalized coherent-entangled state representation |α, p μ,ν is successfully derived via constructing the integration of unity in normally ordered Gaussian operator forms and then decomposing it as projection operators. This is a convenient approach for obtaining new representations. We then prove that |α, p μ,ν has the completeness relation and only partly orthogonal, then discuss how to use a beamsplitter to produce such a state. As its potential application, formulas can be obtained by using the completeness of |α, p μ,ν , which is very important in mathematical physics, especially in quantum optics.

四体纠缠态表象的构建及其应用

利用有序算符乘积内的积分(IWOP)技术,构建了一种四体相容算符1+2+3+4、p1-p2、p1-p3和p1-p4的共同本征态。研究表明,这种量子态具有正交性和完备性,完全可以作为一种新的表象。在动量表象和坐标表象中,对这种量子态进行了Schmidt分解,表明它是一种四体纠缠态。利用这种纠缠态构造了一个新的四模压缩算符,并分析其压缩特性,指出了纠缠与压缩的内在联系。

光束分离器算符的分解特性与纠缠功能

光束分离器是量子光学中的基本线性器件之一，它在量子纠缠态的制备与测量上起着重要作用。基于光束分离器（BS）对算符的矩阵变换关系，本文导出了BS算符在若干表象中的自然表示。利用这个自然表示（而非SU（2）李代数关系）及有序算符内的积分技术，可直接导出BS算符的正规乘积、紧指数表示及多种分解形式。此外，可直接导出一种纠缠态表象及其Schmidt分解。这对于讨论连续变量量子隐形传输是十分方便的。