On the Entangled Fractional Fourier Transform in Tripartite Entangled State Representation

Based on the newly constructed two mutually conjugate 3-mode entangled states of continuum variables in three-mode Fock space we introduce entangled fractional Fourier transform (EFFT) for the tripartite entangled state representations, which are not a direct product of three 1-dimensional FFTs. The eigenmodes of EFFT are obtained,which is different from the usual Hermite polynomials. The EFFT of the three-mode squeezed state is derived.     

On the Entangled Fractional Fourier Transform in Tripartite Entangled State Representation

Based on the newly constructed two mutually conjugate 3-mode entangled states of continuum variablesin three-mode Fock space we introduce entangled fractional Fourier transform (EFFT) for the tripartite entangled staterepresentations, which are not a direct product of three 1-dimensional FFTs. The eigenmodes of EFFT are obtained,which is different from the usual Hermite polynomials. The EFFT of the three-mode squeezed state is derived.     

Entangled Fractional Fourier Transform for the Multipartite Entangled State Representation

We deduce entangled fractional Fourier transformation (EFFT) for the multipartite entangled state representation, which was newly constructed with two mutually conjugate n-mode entangled states of continuum variables in n-mode Fock space. We establish a formalism of EFFT for quantum mechanical wave functions, which provides us a convenient way to derive some wave functions. We find that the eigenmode of EFFT is different from the usual Hermite Polynomials. We also derive the EFFT of the n-mode squeezed state.     

可控三模纠缠相干态的产生

采用量子理论,考虑边界振动的微腔与腔内的三模辐射场构成的系统,给出了系统的时间演化算符及其变换,得到了系统的态函数随时间的演化关系.结果表明,当振动边界回到初态时,三模腔场处于纠缠相干态,并且可以调控不同纠缠相干态的产生.给出了九个不同的三模纠缠相干态,这些态中含有不同的相位因子,这些相位因子充分体现了场和振动边界的相互作用和相互影响.这些结果为可控纠缠相干态的实验制备提供了重要的理论依据.     

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.     

One-Sided Squeezing for Two Special Kinds of Tripartite Entangled States

Based on two mutual conjugate tripartite entangled states $|\eta,\sigma\rangle_\theta$ and $| \varsigma ,\tau\rangle_\theta $ we generalize the two-mode one-sided squeezing operators to three-mode case. We derive how the tripartite entangled states transform under the three-mode squeezing operators. We conclude that the entangled state representations provide a convenient basis for deriving various three-mode squeezing operators.     

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.     

由光分束器和起偏器混合产生的三模纠缠态表象

在三模Fock空间中,本文构建了一种新的三模连续变量纠缠态,它构成了一个新的量子力学表象.该态可以利用非对称光束分离器和起偏器实现.态的纠缠性通过获得其相应的施密特分解得以说明.作为该表象的一个重要应用,利用它实现了单粒子态的量子隐态传输,给出了相应的传输方案. 关键词： 三模连续纠缠态表象 有序算符内的积分技术 量子纠缠 量子隐态传输     

Creation and Destruction of Entanglement via Fourier Multiport Devices

We study entangling and disentangling functions of optical Fourier multiport devices in which input-output relation for the creation and annihilation operators is given by a finite Fourier transform. It is shown that these Fourier multiport devices can act as entanglement converters which can not only create entanglement from an unentangled state at the input but also destroy entanglement in an entangled state at the input. Creation and destruction of two-mode and three-mode entangled coherent states （ECSs） are investigated in detail. The creation and destruction of Bell-type two-mode ECS, GHZ-type and W-type three-mode ECSs are indicated explicitly through using Fourier four-port and six-port devices, respectively.     

A Kind of Three-Mode Entangled States of Continuum Variables Generated by Beam Splitter and Parametric Down-Conversion Amplifier

In three-mode Fock space we find a new tripartite entangled state |α,γ>_λ, which make up a new quantum mechanical representation. The state |α,γ>_λ can be generated by using the setup composing of a beam splitter and a parametric down-conversion amplifier. Application of the state is briefly discussed.     

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.     

A Kind of New Three-Mode Coherent-Entangled State and Its Application

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

Three-Mode Cyclic Squeezed States Constructed via EPR Entangled State

We construct the three-mode cyclic squeezed states and analyze its squeezing property by using the technique of integration within an ordered product of operators and the natural representation of the two-mode squeezing operator in the Einstein-Podolsky-Rosen entangled state basis.     

三粒子纠缠W态隐形传态的正交完备基展开与算符变换

先是对利用单个两粒子及单个三粒子纠缠态作为量子信道实现三粒子纠缠W态的隐形传态方案进行讨论.然后由波函数的叠加原理与算符变换出发,将体系的总量子量按照Bell基展开实现量子隐形传态,给出了变换算符与实际操作算符之间的联系.进一步验证出变换算符可逆是成功实现三粒子纠缠W态隐形传态的必要条件的结论. 关键词： 三粒子纠缠W态 Bell基展开 变换算符 隐形传态     

三粒子纠缠Ｗ态的隐形传态

提出利用三个二粒子纠缠态作为量子信道，实现三粒子纠缠Ｗ态的隐形传态的方案.首先考察量子信道是最大纠缠态的情形，然后进一步考察量子信道是非最大纠缠态的情形.发现在量子信道为非最大纠缠态时，通过引进一个辅助粒子，并构造一个幺正变换矩阵，即可以一定的概率完成三粒子纠缠Ｗ态的隐形传态. 关键词： 隐形传态 三粒子纠缠 纠缠Ｗ态 非最大纠缠量子信道     

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.     

Application of three-mode Einstein-Podolsky-Rosen entangled state with continuous variables to teleportation

We consider how to teleport two- and three-mode Einstein--Podolsky--Rosen entangled states (|\eta> and | p_t,\chi₂,\chi₃>) via a | p_t,\chi₂,\chi₃> quantum channel for continuous variables. Using the complete and orthogonal representation of the entangled states, we can not only find the a complete basis set for the joint measurement but also propose the specific scheme of teleportation. Our calculation can be greatly simplified by using their Schmidt decompositions.     

通过四个纠缠态粒子来实现未知的三个纠缠态粒子的量子几率隐形传输

提出一种分别利用四个三态粒子的最大纠缠态和非最大纠缠态作为量子通道来传输一未知的三个三态粒子纠缠态的方案.首先考察量子通道是最大纠缠态的情况,然后进一步考察量子通道是非最大纠缠态的情况,同时发现在后者情况时,通过引进一个辅助粒子,并构造一幺正变换矩阵,即可以一定的几率完成该三态粒子纠缠态的隐形传输.