Two-mode excited entangled coherent states and their entanglement properties

This paper introduces two types of two-mode excited entangled coherent states (TMEECSs) |Ψ_±(α,m,n)>, studies their entanglement characteristics, and investigates the influence of photon excitations on quantum entanglement. It shows that for the state |Ψ₊(α,m,m)> the two-mode photon excitations affect seriously entanglement character while the state |Ψ_-(α,m,m)> is always a maximally entangled state, and shows how such states can be produced by using cavity quantum electrodynamics and quantum measurements. It finds that the entanglement amount of the TMEECSs is larger than that of the single-mode excited entangled coherent states with the same photon excitation number.     

Quantum Communication with Continuous Variables

Many quantum communication schemes rely on the resource of entanglement. For example, quantum teleportation is the transfer of arbitrary quantum states through a classical communication channel using shared entanglement. Entanglement, however, is in general not easy to produce on demand. The bottom line of this work is that a particular kind of entanglement, namely that based on continuous quantum variables, can be created relatively easily. Only squeezers and beam splitters are required to entangle arbitrarily many electromagnetic modes. Similarly, other relevant operations in quantum communication protocols become feasible in the continuous‐variable setting. For instance, measurements in the maximally entangled basis of arbitrarily many modes can be accomplished via linear optics and efficient homodyne detections. In the first two chapters, some basics of quantum optics and quantum information theory are presented. These results are then needed in Chapter III, where we characterize continuous‐variable entanglement and show how to make it. The members of a family of multi‐mode states are found to be truly multi‐party entangled with respect to all their modes. These states also violate multi‐party inequalities imposed by local realism, as we demonstrate for some members of the family. Further, we discuss how to measure and verify multi‐party continuous‐variable entanglement. Various quantum communication protocols based on the continuous‐variable entangled states are discussed and developed in Chapter IV. These include the teleportation of entanglement (entanglement swapping) as a test for genuine quantum teleportation. It is shown how to optimize the performance of continuous‐variable entanglement swapping. We highlight the similarities and differences between continuous‐variable entanglement swapping and entanglement swapping with discrete variables. Chapter IV also contains a few remarks on quantum dense coding, quantum error correction, and entanglement distillation with continuous variables, and in addition a review of quantum cryptographic schemes based on continuous variables. Finally, in Chapter V, we consider a multi‐party generalization of quantum teleportation. This so‐called telecloning means that arbitrary quantum states are transferred not only to a single receiver, but to several. However, due to the quantum mechanical no‐cloning theorem, arbitrary quantum states cannot be perfectly copied. We present a protocol that enables telecloning of arbitrary coherent states with the optimal quality allowed by quantum theory. The entangled states needed in this scheme are again producible with squeezed light and beam splitters. Although the telecloning scheme may also be used for "local'' cloning of coherent states, we show that cloning coherent states locally can be achieved in an optimal fashion without entanglement. It only requires a phase‐insensitive amplifier and beam splitters.     

Influence of dephasing on the entanglement teleportation via a two-qubit Heisenberg XYZ system

We study the entanglement dynamics of an anisotropic two-qubit Heisenberg XYZ system in the presence of intrinsic decoherence. The usefulness of such a system for performance of the quantum teleportation protocol T₀\mathcal{T}_0 and entanglement teleportation protocol T₁\mathcal{T}_1 is also investigated. The results depend on the initial conditions and the parameters of the system. The roles of system parameters such as the inhomogeneity of the magnetic field b and the spin-orbit interaction parameter D, in entanglement dynamics and fidelity of teleportation, are studied for both product and maximally entangled initial states of the resource. We show that for the product and maximally entangled initial states, increasing D amplifies the effects of dephasing and hence decreases the asymptotic entanglement and fidelity of the teleportation. For a product initial state and specific interval of the magnetic field B, the asymptotic entanglement and hence the fidelity of teleportation can be improved by increasing B. The XY and XYZ Heisenberg systems provide a minimal resource entanglement, required for realizing efficient teleportation. Also, in the absence of the magnetic field, the degree of entanglement is preserved for the maximally entangled initial states $\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {00} \right\rangle \pm } \right|\left. {11} \right\rangle } \right)} \right.$\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {00} \right\rangle \pm } \right|\left. {11} \right\rangle } \right)} \right.. The same is true for the maximally entangled initial states $\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {01} \right\rangle \pm } \right|\left. {10} \right\rangle } \right)} \right.$\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {01} \right\rangle \pm } \right|\left. {10} \right\rangle } \right)} \right., in the absence of spin-orbit interaction D and the inhomogeneity parameter b. Therefore, it is possible to perform quantum teleportation protocol T₀\mathcal{T}_0 and entanglement teleportation T₁\mathcal{T}_1, with perfect quality, by choosing a proper set of parameters and employing one of these maximally entangled robust states as the initial state of the resource.     

Experimental Quantum Teleportation of Laser Beams

We experimentally demonstrate quantum teleportation for continuous variables by using squeezed-state entanglement. A fidelity expression for a real experimental system is presented, where all the imperfection factors are considered, including losses and phase fluctuations. The measured fidelity for input coherent states is 0.62 and the prospective result with our measured entanglement and efficiencies is 0.69. We will show the details of the quantum teleportation for continuous variable and discuss the problems for further improvement in this experiment.     

Quantum teleportation of one－ and two－photon superposition states

Quantum teleportation of one- and two-photon superposition states based on EPR entanglement of continuous-wave two-mode squeezed state is discussed. The fidelities of teleportation axe deduced for two different input quantum states. The dependence of the fidelity on the parameters of EPR entanglement and the gain of the classical channels are shown numerically. Comparing with the teleportation of Fock state and coherent state, it is pointed out that for given EPR entanglement and classical gain, the higher the nonclassicality of the input state, the lower the accessible fidelity of teleportation.     

Quantum teleportation

Quantum Teleportation of one qubit of information using entangled state of two qubit is explained. It is shown that if quantum state of N qubits is to be teleported, the requirement is entangled state of at least 2N qubits. A scheme of teleportation of a superposition of even and odd coherent states was suggested by Van Enk and Hirota for teleportation of superposed coherent state, success of which is ? according to the authors. It is shown how this scheme can be modified so as to make the success nearly 1. It is also explained how decoherence can be taken into account and how such schemas can be applied to similar phenomena of entanglement diversion and entanglement swapping.     

利用单个三粒子最大GHZ态或两个EPR态隐形传送任意三粒子GHZ态

提出利用单个三粒子最大Greenberger-Horne-Zeilinger (GHZ)态或两个Einstein-Podolsky-Rosen (EPR)态作为量子信道确定性隐形传送任意三粒子GHZ态的两个方案，并将方案推广至隐形传送任意n(n≥4)粒子GHZ态的情况.讨论了量子信道受噪声影响时隐形传态的保真度.研究发现，当作为量子信道的单个三粒子最大GHZ态受到噪声影响时，隐形传态的保真度仅与量子信道的纠缠度有关，而当作为量子信道的两个EPR态受到噪声影响时，隐形传态的保真度不仅与量子信道的纠缠度有关，还与待传送态的纠缠度有关.所提出的方案具有节省量子信道纠缠资源的特点. 关键词： 隐形传态 三粒子Greenberger-Horne-Zeilinger态 量子逻辑门 保真度     

Continuous-variable quantum teleportation of even and odd coherent states through varied gain channels

This paper has investigated quantum teleportation of even and odd coherent states in terms of the EPR entanglement states for continuous variables. It discusses the relationship between the fidelity and the entanglement of EPR states, which is characterized by the degree of squeezing and the gain of classical channels. It shows that the quality of teleporting quantum states also depends on the characteristics of the states themselves. The properties of teleporting even and odd coherent states at different intensities are investigated. The difference of teleporting two such kinds of quantum states are analysed based on the quantum distance function.     

Coherent interaction and action-counteraction theory in small polaron systems,and ground state properties

Based on the coherent interaction and action-counteraction principles, we investigate the ground state properties for small polaron systems, the coherent-squeezed fluctuation correction, and the anomalous lattice quantum fluctuation, with the new variational generator containing correlated squeezed-coherent coupling and quantum entanglement. Noting that $-2t $ is the T.B.A. energy, for the coherent interaction effect, we find the ground-state energy $E_0$ to be $-2.428t$, in which the coherent squeezed fluctuation correction $-A_0 t$ is $-0.463t $ (where $ t $ is the hopping integral, $\omega $ is the phonon frequency), with the electron-one-phonon coupling constant $g=$1 and the electron-two-phonon coupling constant $g_{1}=-0.1$. However, as a result of the action-counteraction effect, $\tilde{{E}}_{0} $ is $-2.788t$, but $-\tilde{{A}}_{0} t$ is $-0.735t$. As to the polaron binding energy $(E_{\rm P} )$, for the coherent interaction effect, $E_{\rm P} $ is $-1.38\omega $, but for the action-counteraction effect, $\tilde{{E}}_{\rm P}$ is $-1.88\omega $. In particular, the electron-two-phonon interaction noticeably enlarges the coherent interaction and the coherent squeezed quantum fluctuation correction. By intervening with the quantum entanglement, the evolutions of the squeezed coherent state and the lattice quantum fluctuation begin to take control. At that time, we encounter a new quantum phase coherence phenomenon — the collapse and revival of inversion repeatedly for the coherent state in the entangled evolution.     

利用两能级原子与腔场的相互作用转移纠缠

分析了大失谐情况下一个两能级原子和相干态腔场相互作用的特点;讨论了利用两能级原子和相干态腔场相互作用制备纠缠相干态的方法;提出了一个关于纠缠相干态的纠缠转移的方案。在这个纠缠转移的方案里,通讯伙伴之间使用的量子信道是由两个振幅相同位相相反的相干态构成的纠缠态。通过使用两能级原子和腔肠相干态的相互作用和两模正交态测量并在经典信息的帮助下完成了三个通讯伙伴之间的纠缠转移。随着近来腔量子电动力学技术的发展,这个方案是能够被实行的。     

单-双模组合压缩热态的纠缠性质及在量子隐形传态中的应用

基于单-双模组合压缩真空态一定范围内能够获得压缩增强的效果,引入单-双模组合压缩热态(DSMST),讨论其纠缠性质.利用Weyl编序算符在相似变换下的不变性,简洁方便地导出了DSMST的纠缠度-负对数值,并给出了当热效应存在时保持纠缠的条件.研究表明:与通常的双模压缩态相比,随着参数的增加,DSMST的纠缠度增加.作为DSMST的应用,利用其实现相干态的量子隐形传输.结果表明:不同于纠缠度随压缩参数增加,保真度获得改善是有条件的,该条件恰好就是一正交分量涨落出现压缩增强的参数区域.此外,解析推导了有效隐形传输保真度(1/2)的条件.     

Teleportation of tripartite entangled coherent states

This paper proposes a feasible scheme for the quantum teleportation of tripartite entangled coherent states by using linear optical devices such as beam splitters, phase shifters and photo detectors. The scheme is based on the bipartite maximally entangled coherent state and the tripartite entangled coherent state with bipartite maximal entanglement as quantum channels. It shows that when the mean number of photons is equal to 2, the total minimum of the average fidelity for an arbitrary tripartite entangled state is 1-0.67×10 ^-3.     

三粒子纠缠相干态的隐形传态

提出了一个利用一个两粒子最大纠缠相干态和一个三粒子纠缠相干态作为量子信道进行三粒子纠缠相干态隐形传态的方案.该方案只需线性光学操作和双模光子数测量.计算结果表明,应用本方案的设置,隐形传态成功的概率与所用的相干态的平均光子数有关,反映了纠缠相干态的非正交特性.     

The entropic squeezing of superposition of two arbitrary coherent states

In this paper the superpositions of two arbitrary coherent states ｜ψ〉 = α ｜β｜ ＋ be^iψ ｜mβe^iδ〉 are constructed by using the superposition principle of quantum mechanics. The entropic squeezing effects of the quantum states are studied. The numerical results indicate that the amplitudes, the ratio between the amplitudes of two coherent states, the phase difference between the two components and the relative phase of the two coefficients play important roles in the squeezing effects of the position entropy and momentum entropy.     

Entanglement in a generalized Jaynes--Cummings model

We investigate the pairwise entanglement and global entanglement in a generalized Jaynes--Cummings model, which can be used to realize Greenberger--Horne--Zeilinger (GHZ) entangled state (Zheng S B 2001 {\it Phys. Rev. Lett.} {\bf 87} 230404). Our results show that the W-type entangled states cannot be generated based on the model. The dependences of entanglement on Rabi frequency $\lambda$ and dipole--dipole coupling strength ${\it \Omega}$ are given. It is found that there exists the quantum phase transition when $\lambda={\it \Omega}$. For typical experimental data, the critical temperature for pairwise entanglement is on the order of $10^{-6}$\,K. Based on these results, two strategies that overcome decoherence are proposed.     

Teleportation of a bipartite entangled coherent state via cavity QED

Based on the atom--cavity--field interaction, this paper proposes a scheme for the teleportation of a bipartite entangled coherent state (ECS) with high fidelity as long as $\left| \alpha \right|$ is not too small. In this proposal, only four cavities and a three-level cascade atom are needed. The fidelity of the ECS is calculated and analysed in detail.     

Improving the fidelity of continuous-variable quantum teleportation by tuning displacement gain

The fidelity of teleportation of continuous quantum variables can be improved by tuning the local displacement gain. We investigate the optimization of the fidelity for the teleportation of Schrodinger cat states, and of coherent states. It is found that the gain corresponding to the maximum fidelity is not equal to one for the two input states in the case of the small squeezing degree of the entanglement resource, while unity displacement gain is the best choice for teleporting arbitrary quantum states in the case of large squeezing.     

Entanglement in Bipartite Generalized Coherent States

Entanglement of formation in a class of bipartite generalized coherent states is discussed. It is shown that a positive parameter can be associated with these bipartite states so that the states with equal value for the parameter are of equal entanglement. For the class of states considered, the maximum possible entanglement of one ebit is attained if the value of the positive parameter is . It is shown that the entanglement of formation is one ebit when the relative phase between the composing states is π in the class of bipartite generalized coherent states considered.     

Continuous-variable quantum information processing with squeezed states of light

We investigate experiments of continuous-variable quantum information processing based on the teleportation scheme. Quantum teleportation, which is realized by a two-mode squeezed vacuum state and measurement-and-feedforward, is considered as an elementary quantum circuit as well as quantum communication. By modifying ancilla states or measurement-and-feedforwards, we can realize various quantum circuits which suffice for universal quantum computation. In order to realize the teleportation-based computation we improve the level of squeezing, and fidelity of teleportation. With a high-fidelity teleporter we demonstrate some advanced teleportation experiments, i.e., teleportation of a squeezed state and sequential teleportation of a coherent state. Moreover, as an example of the teleportation-based computation, we build a QND interaction gate which is a continuous-variable analog of a CNOT gate. A QND interaction gate is constructed only with ancillary squeezed vacuum states and measurement-and-feedforwards. We also create continuous-variable four mode cluster type entanglement for further application, namely, one-way quantum computation.     

Long-distance quantum teleportation assisted with free-space entanglement distribution

Faithful long-distance quantum teleportation necessitates prior entanglement distribution between two communicated locations. The particle carrying on the unknown quantum information is then combined with one particle of the entangled states for Bell-state measurements, which leads to a transfer of the original quantum information onto the other particle of the entangled states. However in most of the implemented teleportation experiments nowadays, the Bell-state measurements are performed even before successful distribution of entanglement. This leads to an instant collapse of the quantum state for the transmitted particle, which is actually a single-particle transmission thereafter. Thus the true distance for quantum teleportation is, in fact, only in a level of meters. In the present experiment we design a novel scheme which has overcome this limit by utilizing fiber as quantum memory. A complete quantum teleportation is achieved upon successful entanglement distribution over 967 meters in public free space. Active feed-forward control techniques are developed for real-time transfer of quantum information. The overall experimental fidelities for teleported states are better than 89.6%, which signify high-quality teleportation.