Multi-mode Coherent-Entangled State Representation and Its Applications

We introduce the so-called coherent-entangled state (CES) in the four-mode Fock space, which makes up a new quantum mechanical representation owing to completeness relation and orthogonal property. Its standard Schmidt decomposition and experimental generation using beam-splitter (BS) are proposed. In addition, its applications in quantum optics are presented. Finally, we extend it to multi-mode case and discuss some applications, too.     

Multi-mode Einstein-Podolsky-Rosen Entangled State Representation and Its Applications

Our primary purpose of this work is to explicitly construct the general multiparite Einstein-Podolsky- Rosen （EPR） entangled state in multi-mode Fock space for a system with different masses of particles, which makes up a new quantum mechanical representation owing to completeness relation and orthogonal property. Its entanglement can be seen more clearly by analyzing its standard Schmidt decomposition. In addition, some applications of the multipartite entanglement are proposed including deriving the generalized Wigner operator and squeezing operator.     

Coherent-Entangled State in Three-Mode and Its Applications

We introduce the new concept of coherent-entangled state （CES）. By virtue of the technique of integration within an ordered product of operators we introduce a new kind of three-mode CES [β,γ,x）, which exhibits both properties of the coherent state and the entangled state. [β,γ,x） makes up a new quantum mechancial representation. Its applications in quantum optics are also presented.     

Coherent-Entangled State in Three-Mode and Its Applications

We introduce the new concept of coherent-entangled state (CES). By virtue of the technique of integration Its applications in quantum optics are also presented.     

Multi-mode Einstein-Podolsky-Rosen Entangled State Representation and Its Applications

Our primary purpose of this work is to explicitly construct the general multipartite Einstein-Podolsky-Rosen (EPR) entangled state in multi-mode Fock space for a system with different masses of particles, which makes up a new quantum mechanical representation owing to completeness relation and orthogonal property. Its entanglement can be seen more clearly by analyzing its standard Schmidt decomposition. In addition, some applications of the multipartite entanglement are proposed including deriving the generalized Wigner operator and squeezing operator.     

A generalized two-mode entangled state: Its generation,properties, and applications

Using the technique of integration within an ordered product of operators we construct a generalized two-mode entangled state, which can be generated by an asymmetrical beam splitter （BS）. Some important properties of this state, such as orthogonality and Schmidt decomposition, are also dis- cussed by deriving the expression of BS operator in coordinate representation. As its applications, to conjugate state, obtain operator identities, generate new squeezing operators （squeezed state） are also presented. It is shown that the fidelity of quantum teleportation can be enhanced under certain case by using the asymmetrical new squeezed state as entangled resource.     

New Parameterized Coherent-Entangled State Representation and Its Applications

Based on EPR’s idea of quantum entanglement, new parameterized coherent-entangled states |α,p〉 _μ,ν are introduced in two-mode Fock space, which can be implemented by using a beam splitter. Possible superpositions of |α,p〉 _μ,ν result in some new entangled states. The asymmetric ket-bra integration from |α,p〉 _μ,ν leads to a new one- and two-mode combinatorial squeezing operator with stronger squeezing, which clearly shows the intrinsic relationship between squeezing mechanism and quantum entanglement.     

Three-Mode Entangled State Representation of Continuum Variables and Optical Four-Wave Mixing

We establish a new three-mode entangled state representation , of continuum variables, which make up a complete set. Using optical four-wave mixing and a beam splitter transform we can prepare , . Based on , a new number-difference--operational-phase uncertainty relation is established and the corresponding squeezing dynamics is discussed.     

Complex-Variable Fokker-Planck Equation Solved in Entangled State Representation

We lind that the Fokker-Planck equation in complex variables can be conveniently solved in the context of bipartite entangled state representation and its relationship with SU（2） Lie algebraic generators＇ new realization {（1/4）[（Q1 - Q2）^2 ＋ （P1＋ P2）^2], （1/4）[（Q1 ＋Q2）^2＋ （P1 - P2）^2], and -（i/2）（Q1P2 ＋ Q2P1）}, the quadratic combination of canonical operators.     

Four-Particle Entangled State Representation and Its Squeezing Transformation

The four-particle EPR entangled state | p,χ₂,χ₃,χ₄〉is constructed. The corresponding quantum mechanical operator with respect to the classical transformation p→e^λ₁p, χ₂→ e^λ₂χ₂, χ₃→e^λ₃χ₃, and χ₄→e^λ₄χ₄ in the state |p,χ₂ ,χ₃ ,χ₄〉is investigated, and the four-mode realization of the SU(1,1) Lie algebra as well as the corresponding squeezing operators are presented.     

Four-mode coherent-entangled state and its application

A new kind of four-mode continuous variable coherent-entangled state is proposed in the Fock space by using the technique of integration within an ordered product, which exhibits both the properties of a coherent state and an entangled state, and spans a complete and orthonormal representation. The conjugate state of the four-mode continuous variable coherent-entangled state is derived by using the Fourier transformation. Moreover, a simple experimental protocol of generating a four-mode continuous variable coherent-entangled state is proposed by using beam splitters. As applications of this four-mode continuous variable coherent-entangled state, a four-mode entangled state and a four-mode squeezing-Fresnel operator are constructed.     

Four-mode coherent-entangled state and its application

A new kind of four-mode continuous variable coherent-entangled state is proposed in the Fock space by using the technique of integration within an ordered product,which exhibits both the properties of a coherent state and an entangled state,and spans a complete and orthonormal representation.The conjugate state of the four-mode continuous variable coherent-entangled state is derived by using the Fourier transformation.Moreover,a simple experimental protocol of generating a four-mode continuous variable coherent-entangled state is proposed by using beam splitters.As applications of this four-mode continuous variable coherent-entangled state,a four-mode entangled state and a four-mode squeezing-Fresnel operator are constructed.     

Deformation of Superoperator's Kraus Representation Derived by Weyl Correspondence and Entangled State Representation

By virtue of the Weyl correspondence and based on the the technique of integration within an ordered product of operators, we show under what condition the superoperator's Kraus representation ρ^ˊ=∑_μ A_μρA_μ^† can be deformed as ρ^ˊ=(1/π)∫d²αB(α)D(α)ρD^†(α), where D(α) is the displacement operator, B(α) is a probability density related to the classical Weyl correspondence of A_μ. An alternate discussion by using the entangled state representation and through a quantum teleportation process is also presented.     

Solution to Operator Fredholm Equation in Bipartite Entangled State Representation and Its Applications

Based on the bipartite entangled state representation and using the technique of integration within an ordered product （IWOP） of operators we construct the corresponding operator Fredholm equations and then derive their solutions. As its application we deduce some new bosonic operator identities and new relations about the two-variable Hermite polynomials.     

Representation of the coherent state for a beam splitter operator and its applications

A beam splitter operator is a very important linear device in the field of quantum optics and quantum information. It can not only be used to prepare complete representations of quantum mechanics, entangled state representation, but it can also be used to simulate the dissipative environment of quantum systems. In this paper, by combining the transform relation of the beam splitter operator and the technique of integration within the product of the operator, we present the coherent state representation of the operator and the corresponding normal ordering form. Based on this, we consider the applications of the coherent state representation of the beam splitter operator, such as deriving some operator identities and entangled state representation preparation with continuous-discrete variables. Furthermore, we extend our investigation to two single and two-mode cascaded beam splitter operators, giving the corresponding coherent state representation and its normal ordering form. In addition, the application of a beam splitter to prepare entangled states in quantum teleportation is further investigated, and the fidelity is discussed. The above results provide good theoretical value in the fields of quantum optics and quantum information.     

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.     

基于p1-p2与a1+a2共同本征态的相干纠缠态表象的构建及性质

利用有序算符乘积内的积分技术（IWOP）,建立了一种称之为相干纠缠态的两粒子体系的新表象,研究了这种新表象的性质,从理论上探讨了这种相干纠缠态的产生方法.结果表明：本文建立的这种p₁-p₂与a₁+a₂的共同本征态|p,β〉,既具有相干态的特性,又体现了纠缠态的特征,具有超完备性,完全可以作为一个表象使用. 物理上可以用光分束器来实现|< 关键词： IWOP技术 相干纠缠态表象 分束器     

On the Entangled State Representation with Continuum Variables

we propose the conception of entangled state representation with continuum variables. We analyze the non-factorizable properties of the |η> state, the common eigenvector of two-particle relative position and total moment um (Fan Hongyi and J.R. Klauder, Phys. Rev. A49 (1994) 704), and recast it into the standard form as the state prepared in a parametric down conversion process which involves the entanglement of idle and signal photons. We name the set of |η> as entangled state representation, as it is orthonormal and complete     

Angular Momentum Phase State Representation for Quantum Pendulum

To consummate the quantum pendulum theory whose Hamiltonian takes bosonic operator formalism and manifestly exhibits its dynamic behaviour in the entangled state representation, we introduce angular momentum state representation and phase state representation. It turns out that the angular momentum state is the partial wave expansion of the entangled state.     

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。