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.     

Efficient preparation of a four-photon cluster state with homodyne measurement via cross-Kerr nonlinearity

A scheme is proposed for generating a multiphoton entangled cluster state among four modes. The scheme only uses Kerr medium, beam splitter and homodyne measurements on coherent light fields, which can be efficiently made in quantum optical laboratories. The photon in the signal mode is prepared in a superposition state of the vacuum state and one-photon state while the probe beam is initially set in a coherent state superposition. The strong probe mode interacts successively with multiple signal-mode photo...     

Generating Entangled State of Photons with Beam Splitter

We demonstrate how to generate entangled state of photons with beam splitter. Its shown that we can generate entangled state by adjusting appropriately the reflectivity, the phase difference and choosing the initial state.     

Experimental measurement of covariance matrix of two-mode entangled state

A two-mode entangled state was generated experimentally through mixing two squeezed lights from two optical parametric amplifiers on a 50/50 beam splitter.The entangled beams were measured by means of two pairs of balanced homodyne detection systems respectively.The relative phases between the local beams and the detected beams can be locked by using the optical phase modulation technique.The covariance matrix of the two-mode entangled state was obtained when the relative phase of the local beam and the detected beam in one homodyne detection system is locked and the other is scanned.This method provides a way by which one can extract the covariance matrix of any selected quadrature components of two-mode Gaussian state.     

级联光束分离器的纠缠特性及其应用

光束分离器是一个具有广泛应用的线性光学器件,它在非经典量子态特别是纠缠态的制备中具有重要作用.基于单个光束分离器的表象表示,本文进一步考察多个级联光束分离器的纠缠特性,特别是结合有序算符内的积分技术推导了级联光束分离器的正规乘积、紧指数表示及级联算符的表象表示.作为应用,本文利用两个级联光束分离器获得了量子力学表象及其Schmidt分解,并结合量子条件测量制备了qubit态的叠加态.本文的研究方法已被直接推广至多个光束分离器级联情况,相关研究内容为多模纠缠态、多模qubit态的制备提供了一种有效的途径,且为由光束分离器组成的线性器件系统总作用的算符正规乘积及其紧指数表示提供了一般方法.     

单光分束器的量子变换算符研究

针对理想情况下单光分束器,得到了其对应的变换矩阵.用相干态表象和有序算符内积分技术,给出其对应的幺正变换算符.纠缠态的实验制备方案,说明单光分束器在量子信息源研究中具有十分重要的作用.     

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. 关键词： 光束分离器算符 纠缠态表象 有序算符内的积分技术 Schmidt分解     

A new bipartite entangled state describing the parametric down-conversion process and its applications in quantum optics

We construct a new bipartite entangled state(NBES),which describes both the squeezing and the entanglement involved in the parametric down-conversion process and can be produced using a symmetric beam splitter.Constructing asymmetric ket-bra integrations based on the NBES leads to some new squeezing operators,which clearly exhibit the relationships between squeezing and entangled state transformations.Moreover,an entangled Wigner operator with a definite physical meaning is also presented.     

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.     

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.     

线性网络对光场量子态的变换

给出各种输入态和光学器件的数学表述，态包括单光子的空间和极化模，双光子的可分离态和纠缠态，光学器件有分束器，极化分束器，波片．用这种表述对一些重大实验的网络进行分析和计算，其中有Hadamard门的实现，M～Z干涉仪光路分析，Hong-0u—Mandel干涉仪，而且自然引入了Mandel新近名Optical Coherence and Quantum Optics中人为添加的因子，还有Teleportation实验中的Bell基的测量和一些自己设计的网络．并同时给出一些物理上的总结．     

Engineering Two-Mode Non-Gaussian States with Vortex Structures Using a Beam Splitter

Vortex structure and entanglement properties of output field from a beam splitter are investigated. With a n-photon Fock state and a coherent state as the inputs, it is found that the output state before a beam splitter bears a vortex structure in quadrature space and is always entangled and non-classical based on the linear entropy criterion and the P-function analysis in phase space.     

Conditional preparation of X (2) macroscopic entangled states

Two experimental arrangements consisting of coupled spontaneous parametric down-converters with type-I phase matching pumped simultaneously by a powerful optical field in a coherent state through a balanced beam splitter and linear optical elements are proposed for conditional preparation of macroscopic entangled states in output pumping modes of the studied system. Successful generation of the macroscopic entangled state in the pumping modes is unambiguously heralded by coincident detection of two photons in the generated signal and idler modes of the system. We calculate the amount of entanglement and probabilities of successfully observing the X ⁽²⁾ macroscopic entangled states in the total wavefunction. We show that the proposed schemes can be used to obtain a new type of macroscopic entangled states. The text was submitted by author in English.     

A simple scheme for conditional generation of macroscopic entangled states using χ nonlinearity

Experimental arrangement consisting of spontaneous parametric down converter with type-I phase matching (SPDCI) and a beam splitter with unitary Hadamard transformation is proposed for conditional preparation of macroscopic entangled states. The given method requires no photon number resolving detection to generate most probable macroscopic entangled state. We calculate the amount of entanglement stored in the macroscopic entangled states and develop a method to increase the amount of entanglement stored in the state.     

基于N-Λ型原子系统的1→N型分束器

分析N-Λ型原子系统的原子极化率,结果表明即使在全共振条件下,EIT效应并不一定产生,介质对信号场的色散和吸收关系与所有场的复拉比频率有关。信号场传播方程的解析分析表明,此系统可以把一束光分成不同频率的N束光,并且其强度和相位是可控的。暗态极化子分析表明它还可以用作1→N量子分束器,产生多体纠缠态。     

Entanglement concentration for W-type entangled coherent states

An entangled coherent state(ECS) is one type of entanglement, which is widely discussed in the application of quantum information processing(QIP). In this paper, we propose an entanglement concentration protocol(ECP) to distill the maximally entangled W-type ECS from the partially entangled W-type ECS. In the ECP, we adopt the balanced beam splitter(BS) to make the parity check measurement. Our ECP is quite different from the conventional ECPs. After performing the ECP, not only can we obtain the maximally entangled ECS with some success probability, but also we can increase the amplitude of the coherent state. Therefore, it is especially useful in long-distance quantum communication, if the photon loss is considered.     

多个量子节点确定性纠缠的建立

量子纠缠是一种重要的量子资源,在多个空间分离的量子存储器间建立确定性的量子纠缠,然后在用户控制的时刻将所存储的量子纠缠转移到量子信道中进行信息的分发和传送,这对于实现量子信息网络是至关重要的.本文介绍了用光学参量放大器制备与铷原子D1吸收线对应的非经典光场,而且在三个空间分离的原子系综中确定性量子纠缠的产生、存储和转移.利用电磁感应透明光和原子相互作用的原理,将制备的多组分光场纠缠态模式映射到三个远距离的原子系综以建立原子自旋波之间的纠缠.然后,存储在原子系综中的纠缠态通过三个量子通道,纠缠态的量子噪声被转移到三束空间分离的正交纠缠光场.三束释放的光场间纠缠的存在验证了该系统具有保持多组分纠缠的能力.这个方案实现了三个量子节点间的纠缠,并且可以直接扩展到具有更多节点的量子网络,为未来实现大型量子网络通信奠定了基础.     

The dark-state polaritons of a double-Λ atomic ensemble

We study the interaction of two quantized fields with a double-Λ system driven by two classical control fields with variable complex Rabi frequencies. There exists one normal mode of the quantum fields that propagates without absorption. In the two-mode case of dark-state polaritons, we discuss the possibility of storing and retrieving the quantum state in this normal mode. This system can be also used to generate entangled state and, furthermore, it can act as a controllable beam splitter.     

纠缠压缩真空态的纠缠转移

通过分析光学分束器对压缩真空态光场的作用,发现如果分束器的输入光是两束具有同样振幅和相位的单模压缩真空态光场,则输出光为双模压缩真空态光场;若分束器的输入光是两束具有同样振幅但有π相位差的单模压缩真空态光场,则输出光仍为两束单模压缩真空态光场.对于双模压缩真空态光场,每个模中容纳的光子数可以是基数或偶数.而对于单模压缩真空态光场,每个模中只能包含偶数个光子.根据这些结果,提出了一个纠缠转移的方案.在这个方案中,两个纠缠压缩真空态光场被用作量子信道,通过利用光学分束器作用和光子数探测的方法,并在经典通讯的帮助下,实现了三个通讯伙伴之间的纠缠转移.     

Unknown State Transmission Using GHZ States via Collective Noise Channel

Two protocols for transmitting an unknown single-photon state and anunknown non-maximally entangled EPR state are presented by using thequantum channel of three-phonton GHZ (Greenberger-Horne-Zeilinger)state, which can be realized with unitary success probability whencollective noise is taken into account. The protocols can also begeneralized to transmit multi-photon state or to realize quantumcommunication in collective noise channel.