Some New Properties of Wigner Function Studied in Entangled State Representation

Based on the Wigner operator in the entangled state representation we study some new important properties of Wigner function for bipartite entangled systems, such as size of an entangled state, upper bound of Wigner functions, etc. These discussions demonstrate the beauty and elegance of the entangled state representation.     

Nonlinear Tripartite Entangled State Representation and Related Generalized Wigner Function

We construct the nonlinear tripartite entangled state representation and the related generalized Wigner operator. Then we discussed the Wigner functions of the nonlinear tripartite entangled state and the three-mode nonlinear squeezed vacuum state, and obtained the classical Weyl corresponding function of the three-mode nonlinear squeezed state.     

Nonlinear Tripartite Entangled State Representation and Related Generalized Wigner Function

We construct the nonlinear tripartite entangled state representation and the related generalized Wigner operator. Then we discussed the Wigner functions of the nonlinear tripartite entangled state and the three-mode nonlinear squeezed vacuum state, and obtained the classical Weyl corresponding function of the three-mode nonlinear squeezed state.     

On Fermionic Entangled State Representation and Fermionic Entangled Wigner Operator

By analogy with the bosonic bipartite entangled state we construct fermionic entangled state with the Grassmann numbers. The Wigner operator in the fermionic entangled state representation is introduced, whose marginal distributions are understood in an entangled way. The technique of integration within an ordered product (IWOP) of Fermi operators is used in our discussion.     

On Fermionic Entangled State Representation and Fermionic Entangled Wigner Operator

By analogy with the bosonic bipartite entangled state we construct fermionic entangled state with the Grassmann numbers. The Wigner operator in the fermionic entangled state representation is introduced, whose marginal distributions are understood in an entangled way. The technique of integration within an ordered product （IWOP） of Fermi operators is used in our discussion.     

Effective Approach to Constructing n-Mode Wigner Operator in the Entangled State Representation

By extending Fan-Klauder entangled state representation to multipartite case. We construct n-mode Wigner operator in the common eigenvector of the multipartite centre-of-mass coordinate and two mass-weighted relative momenta, and its canonical conjugate state, they are both more complicated entangled state of continuum variables. the technique of integration within an ordered product (IWOP) of operators is essential in our derivation.     

基于纠缠态表象和自旋相干态的新复变函数空间

本文利用有序算符内的积分(IWOP)技术,构造了一个基于单变量厄米多项式H2j(ξ*+τξ/2√τ)的新复变函数空间,该空间与纠缠态表象及施温格玻色环境下的自旋相干态有关。推导出了包含二元厄米多项式的二项式定理,有助于构造新的复变函数空间。同时还提出了一种新的基于H2j(ξ*+τξ/2√τ)的积分变换及其逆变换,这对于推导某些算符恒等式是很有用的。     

New Approach for Calculating Wigner Functions of Generalized Two-Mode Squeezed State and Squeezed Number State via Entangled State Representation

We construct the generalized squeezed vacuum state by virtue of the entangled state 〈η| [Fan Hongyi and J.R. Klauder, Phys. Rev. A47 (1994) 777] and derive the quantum fluctuation of the two-mode quadrature operators.We then calculate Wigner functions of the two-mode squeezed number states and generalized squeezing vacuum state in literature before.     

A Kind of Four-Mode Nonlinear Entangled State Representation in Quantum Optics

Based on the technique of integration within an ordered product of nonlinear bosonic operators, we construct a new four-mode nonlinear entangled state | α,β,γ〉 _λ,μ in 4-mode Fock space, which can make up a complete set. Its properties and applications are discussed. A possible scheme to generate this state is also presented.     

Wigner Distribution Function and Husimi Function of a Kind of Squeezed Coherent State

We find a new x-parameter squeezed coherent state （p, q）κ representation, which possesses well-behaved features, i.e., its Wigner function＇s marginal distribution in the ＂q-direction＂ and in the ＂p-direction＂ is the Gauss/an form exp（-κ（q＇ - q）2}, and exp{（p＇ - p）2/κ}, respectively. Based on this, the Husimi function of（p, q）κ is also obtained, which is a Gauss/an broaden version of the Wigner function. The （P, q）κ state provides a good representative space for studying various properties ot the Husimi operator.     

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.     

Continuous Multipartite Entangled Representation and Its Wigner Operator and Marginal Distribution

By extending the EPR bipartite entanglement to multipartite case, we briefly introduce a continuous multipartite entangled representation and its canonical conjugate state in the multi-mode Fock space, analyze their Schmidt decompositions and give their entangling operators. Furthermore, based on the above analysis we also find the n-mode Wigner operator. In doing so we may identify the physical meaning of the marginal distribution of the Wigner function.     

Continuous Multipartite Entangled Representation and Its Wigner Operator and Marginal Distribution

By extending the EPR bipartite entanglement to multipartite case, we briefly introduce a continuous multipartite entangled representation and its canonical conjugate state in the multi-mode Fock space, analyze their Schmidt decompositions and give their entangling operators. Furthermore, based on the above analysis we also find the n-mode Wigner operator. In doing so we may identify the physical meaning of the marginal distribution of the Wigner function.     

Hermitian Operators Conjugate to Two-Mode Number-Difference Operator Studied in Entangled State Representation

In similar to the derivation of phase angle operator conjugate to the number operator by Arroyo Carrasco- Moya Cessay we deduce the Hermitian phase operators that are conjugate to the two-mode number-difference operator and the three-mode number combination operator. It is shown that these operators are on the same footing in the entangled state representation as the one of Turski in the coherent state representation.     

Hermitian Operators Conjugate to Two-Mode Number-Difference Operator Studied in Entangled State Representation

In similar to the derivation of phase angle operator conjugate to the number operator by Arroyo Carrasco-Moya Cessay we deduce the Hermitian phase operators that are conjugate to the two-mode number-difference operator and the three-mode number combination operator. It is shown that these operators are on the same footing in the entangled state representation as the one of Turski in the coherent state representation.     

引入Wigner函数,Weyl对应和Wigner算符相干态表象的新途径

用坐标、动量完备性的正规乘积内积分形式直接地引入了Wigner函数和Wigner算符的相干态表象,简洁地阐述了它与Weyl对应的关系。     

Study Hankel Transforms and Properties of Bessel Function via Entangled State Representation Transformation in Quantum Mechanics

In Phys. Lett. A 313 (2003) 343 we have found that the self-reciprocal Hankel transformation (HT) is embodied in quantum mechanics by a transform between two entangled state representations of continuum variables. In this work we study Hankel transforms and properties of Bessel function via entangled state representations' transformation in quantum mechanics.     

Wigner Function and Phase Probability Distribution of q-Analogue of Squeezed One-Photon State

In this paper, in terms of the technique of integration within an ordered product （IWOP） of operators and the properties of the inverses of q-deformed annihilation and creation operators, normalizable q-analogue of the squeezed one-photon state, which is quite different from one introduced by Song and Fan [Int. 3. Theor. Phys. 41 （2002） 695], is constructed. Moreover, the Wigner function and phase probability distribution of q-analogue of the squeezed one-photon state are examined.     

Entanglement Involved in Pair Coherent State Studied via Wigner Function Formalism

We calculate Wigner function, tomogram of the pair coherent state by using its Sehmidt decomposition in the coherent state representation. It turns out that the Wigner function can be seen as the quantum entanglement （QE） between two two-variable Hermite polynomials （TVHP） and the tomogram is further simplified as QE of two single-variable Hermite polynomials. The Husimi function of pair coherent state is also calculated.     

Solving Laguerre-Gauss Mode Eigenvectors and Eigenfunctions in Entangled State Representation

We solve the Laguerre-Gauss mode eigenvectors and eigenfunctions in the entangled state representation by searching for common eigenvectors of the 2-dimensional harmonic oscillator's total energy operator and the angular momentum operator. We find that in the entangled state representation the eigen-solution satisfies the Hukuhara equation, and its solution is confluent hypergeometric function.