Quantum fidelity for Gaussian states describing the evolution of open systems

Using the expression of the fidelity for the most general Gaussian quantum states, the quantum fidelity is studied for the states of a harmonic oscillator interacting with an environment, in particular with a thermal bath. The time evolution of the considered system is described in the framework of the theory of open systems based on quantum dynamical semigroups. By taking a correlated squeezed Gaussian state as initial state, we calculate the quantum fidelity for both undisplaced and displaced states. The time evolution of the quantum fidelity is analyzed depending on the squeezing and correlation parameters characterizing the initial Gaussian state and on the dissipation constant and temperature of the thermal bath.     

Fidelity between Gaussian mixed states with quantum state quadrature variances

In this paper, from the original definition of fidelity in a pure state, we first give a well-defined expansion fidelity between two Gaussian mixed states. It is related to the variances of output and input states in quantum information processing. It is convenient to quantify the quantum teleportation(quantum clone) experiment since the variances of the input(output) state are measurable. Furthermore, we also give a conclusion that the fidelity of a pure input state is smaller than the fidelity of a mixed input state in the same quantum information processing.     

Quantifying nonclassicality of one-mode Gaussian states of the radiation field

We define the degree of nonclassicality of a one-mode Gaussian state of the quantum electromagnetic field in terms of the Bures distance between the state and the set of all classical one-mode Gaussian states. We find the closest classical Gaussian state and the degree of nonclassicality using a recently established expression for the Uhlmann fidelity of two single-mode Gaussian states. The decrease of nonclassicality under thermal mapping is carefully analyzed. Along the same lines, we finally present the evolution of nonclassicality during linear amplification.     

Realistic teleportation of coherent states using squeezed vacuum states

This paper presents a realistic scheme for the teleportation of coherent states in which a two-mode squeezed vacuum state serves as the quantum channel and the position-sum and momentum-difference of two local modes serve as the measuring observables. The average fidelity of the teleportation of coherent states is derived for finite squeezing parameters and it turns out that fidelity greater than 1/2 cannot be achieved by using a classical channel alone and the probability distribution of the measurement result is a Gaussian distribution around the unknown parameter of the input coherent state with a width given by the squeezing parameter.     

耗散系统中实现原子态量子隐形传态的保真度

本文运用全量子理论并结合数值计算方法,研究了压缩真空库中利用原子纠缠态作为量子通道实现原子态量子隐形传态的保真度,讨论了被传送的原子初态形式以及压缩库的压缩参数r对保真度的影响.研究表明:当只有输入态受噪声影响,则被传送的初始态中基态概率越大的态,保真度越高;而当量子通道受影响时,则基态和激发态概率相等的原子叠加态传送的保真度最大. 关键词： 量子隐形传态 压缩真空库 保真度     

Non-Gaussian cloning of quantum coherent states is optimal

We consider the optimal cloning of quantum coherent states with single-clone and joint fidelity as figures of merit. While the latter is maximized by a Gaussian cloner, the former is not: the optimal single-clone fidelity for a symmetric 1-to-2 cloner is 0.6826, compared to 2/3 in a Gaussian setting. This cloner can be realized with an optical parametric amplifier and certain non-Gaussian bimodal states. Finally, we show that the single-clone fidelity of the optimal 1-to-infinity cloner is 1/2. It is achieved by a Gaussian scheme and cannot be surpassed even with supplemental bound entangled states.     

Quantum fluctuations in holographic teleportation of optical images

We investigate in detail the quantum fluctuations in the quantum holographic teleportation protocol that we recently proposed [11]. This protocol implements a continuous variable teleportation scheme that enables the transfer of the quantum state of spatially multimode electromagnetic fields, preserving their quantum correlations in space-time, and can be used to perform teleportation of 2D optical images. We derive a characteristic functional, which provides any arbitrary spatio-temporal correlation function of the teleported field, and calculate the fidelity of the teleportation scheme for multimode Gaussian input states. We show that for multimode light fields one has to distinguish between a global and a reduced fidelity. While the global fidelity tends to vanish for teleportation of fields with many degrees of freedom, the reduced fidelity can be made close to unity by choosing properly the number of essential degrees of freedom and the spatial bandwidth of the EPR beams used in the teleportation scheme.Received: 16 March 2004, Published online: 11 May 2004PACS: 03.67.-a Quantum information - 03.65.Bz Foundations, theory of measurement, miscellaneous theories (including Aharonov-Bohm effect, Bell inequalities, Berrys phase) - 42.50.Dv Nonclassical states of the electromagnetic field, including entangled photon states; quantum state engineering and measurements     

与光场依赖强度耦合下运动纠缠双原子的周期量子回声

本文将Tavis-Cummings(T-C)模型推广到同时考虑原子运动及与光场依赖强度耦合的情况.运用全量子理论,研究了与光场依赖强度耦合下运动纠缠双原子量子态保真度演化.采用数值计算的方法,探讨了双原子初始纠缠因子θ、光场平均光子数n以及场模结构参量p对双原子量子态保真度演化的影响,解析分析了双原子周期量子回声的形成规律,揭示了其物理实质.结果表明, 在场模结构参量p=1的情况下,无论光强和双原子初始纠缠因子如何取值,双原子均产生周期2π的量子回声;在强相干场n=30条件下,改变p从1到小于800时,Bell态双原子产生2π/p周期量子回声.当p≥800时,无论光场是真空场、弱相干场或强相干场,双原子量子态保真度恒为1,即第一类Bell态原子持续处于保真态;而当双原子初始纠缠因子为3π/4时,无论n、p取何值,双原子量子态保真度保持为1,双原子持续处于第二类Bell态的保真态.其结论表明, 该推广模型具有很好的双原子周期量子回声性质,为纠缠双原子信息高保真输出及噪音环境下量子信息处理的实验实现提供了理论参量和物理载体.     

耗散腔中两二能级原子态的自旋压缩,量子Fisher信息和最大自旋涨落

在能量耗散腔中,原子用泡利算符描述,光场用相干态描述,运用密度矩阵理论,得到了两二能级原子密度矩阵元的演化规律,分析了与单模辐射场作用过程中原子态的自旋压缩、量子Fisher信息和最大自旋涨落.结果表明:自旋压缩,大于 的最大自旋涨落可以作为量子纠缠的充分必要判据.自旋压缩, 大于 的最大自旋涨落和量子纠缠,它们互相等价.大于1的Fisher信息与它们之间没有等价关系,但可以作为自旋压缩和量子纠缠的充分判据.     

耗散腔中两二能级原子态的自旋压缩量子Fisher信息和最大自旋涨落

在能量耗散腔中,原子用泡利算符描述,光场用相干态描述,运用密度矩阵理论,得到了两二能级原子密度矩阵元的演化规律,分析了与单模辐射场作用过程中原子态的自旋压缩、量子Fisher信息和最大自旋涨落.结果表明:自旋压缩,大于1/2的最大自旋涨落可以作为量子纠缠的充分必要判据.自旋压缩,大于1/2的最大自旋涨落和量子纠缠,它们互相等价.大于1的Fisher信息与它们之间没有等价关系,但可以作为自旋压缩和量子纠缠的充分判据.     

几类相干态的量子保真度

在坐标表象下,研究了几类相干态的量子保真度,对于相干态,我们给出了量子保真度的解析表达式,考查了谐振子特征长度 ,平移距离 对保真度的影响;对于相干态 与 的叠加态,考查了初态量子干涉对量子保真度的影响,结论表明：量子保真度呈周期性;与相干态的量子保真度比较而言,当谐振子处于第二类相干态时,量子干涉能抑制量子态失真,当谐振子处于第三类相干态时,量子干涉能抑制量子态失真,也可能加大量子态失真.     

General Single-Mode Gaussian Operation with Two-Mode Entangled State

Realizing the logic operations with small-scale states is pursued to improve the utilization of quantum resources and to simplify the experimental setup. We propose a scheme to realize a general single-mode Gaussian operation with a two-mode entangled state by utilizing only one nondegenerate optical parametric amplifier and by adjusting four angle parameters. The fidelity of the output mode can be optimized by changing one of the angle parameters.This scheme would be utilized as a basic efficient element in the future large-scale quantum computation.     

Nonlocality criteria for quantum teleportation

An upper bound for the fidelity of quantum teleportation explainable by local hidden variables is derived. This bound is larger than the fidelity corresponding to product states, i.e. to local quantum states. This is relevant for the study of mixed states. In particular, the fidelity of Werner's mixed state, known to be larger than the fidelity of product states, is found to be smaller than the fidelity explainable by local hidden variables. Hence the fidelity of Werner's mixed state does not exhibit nonclassical aspects.     

Quantum information transmission in the quantum wireless multihop network based on Werner state

Many previous studies about teleportation are based on pure state. Study of quantum channel as mixed state is more realistic but complicated as pure states degenerate into mixed states by interaction with environment, and the Werner state plays an important role in the study of the mixed state. In this paper, the quantum wireless multihop network is proposed and the information is transmitted hop by hop through teleportation. We deduce a specific expression of the recovered state not only after one-hop teleportation but also across multiple intermediate nodes based on Werner state in a quantum wireless multihop network. We also obtain the fidelity of multihop teleportation.     

Cloning of continuous quantum variables

The cloning of quantum variables with continuous spectra is analyzed. A Gaussian quantum cloning machine is exhibited that copies equally well the states of two conjugate variables such as position and momentum. It also duplicates all coherent states with a fidelity of 2/3. More generally, the copies are shown to obey a no-cloning Heisenberg-like uncertainty relation.     

与光场依赖强度耦合下运动纠缠双原子的周期量子回声

本文将Tavis-Cummings (T-C)模型推广到同时考虑原子运动及与光场依赖强度耦合的情况.运用全量子理论,研究了与光场依赖强度耦合下运动纠缠双原子量子态保真度演化.采用数值计算的方法,探讨了双原子初始纠缠因子θ、光场平均光子数n以及场模结构参量p对双原子量子态保真度演化的影响,解析分析了双原子周期量子回声的形成规律,揭示了其物理实质.结果表明,在场模结构参量p=1的情况下,无论光强和双原子初始纠缠因子如何取值,双原子均产生周期2π的量子回声;在强相干场n=30条件下,改变P从1到小于800时,Bell态双原子产生2π/P周期量子回声.当p≥800时,无论光场是真空场、弱相干场或强相干场,双原子量子态保真度恒为1,即第一类Bell态原子持续处于保真态;而当双原子初始纠缠因子为3π/4时,无论n、p取何值,双原子量子态保真度保持为1,双原子持续处于第二类Bell态的保真态.其结论表明,该推广模型具有很好的双原子周期量子回声性质,为纠缠双原子信息高保真输出及噪音环境下量子信息处理的实验实现提供了理论参量和物理载体.     

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     

Fidelity matters: the birth of entanglement in the mixing of Gaussian states

We address the interaction of two Gaussian states through bilinear exchange Hamiltonians and analyze the correlations exhibited by the resulting bipartite systems. We demonstrate that entanglement arises if and only if the fidelity between the two input Gaussian states falls under a threshold value depending only on their purities, first moments, and the strength of the coupling. Our result clarifies the role of quantum fluctuations (squeezing) as a prerequisite for entanglement generation and provides a tool to optimize the generation of entanglement in linear systems of interest for quantum technology.     

Continuous variable quantum teleportation with sculptured and noisy non-Gaussian resources

We investigate continuous variable (CV) quantum teleportation using relevant classes of non-Gaussian states of the radiation field as entangled resources. First, we introduce the class two-mode squeezed symmetric superposition of Fock states, including finite truncations of twin-beam Gaussian states as special realizations. These states depend on a set of free independent parameters that can be adjusted for the optimization of teleportation protocols, with an enhancement of the success probability of teleportation both for coherent and Fock input states. We show that the optimization procedure reduces the entangled resources to truncated twin beam states, which thus represents an optimal class of non-Gaussian resources for quantum teleportation. We then introduce a further class of two-mode non-Gaussian entangled resources, in the form of squeezed cat-like states. We analyze the performance and the properties of such states when optimized for (CV) teleportation, and compare them to the optimized squeezed Bell-like states introduced in a previous work [12]. We discuss how optimal resources for teleportation are characterized by a suitable balance of entanglement content and squeezed vacuum affinity. We finally investigate the effects of thermal noise on the efficiency of quantum teleportation. To this aim, a convenient framework is to describe noisy entangled resources as linear superpositions of non-Gaussian state and thermal states. Although the presence of the thermal component strongly reduces the teleportation fidelity, noisy non-Gaussian states remain preferred resources when compared to noisy twin-beam Gaussian states.     

Quantum freeze of fidelity decay for chaotic dynamics

We show that the mechanism of quantum freeze of fidelity decay for perturbations with a zero time average, recently discovered for a specific case of integrable dynamics [New J. Phys. 5, 109 (2003)], can be generalized to arbitrary quantum dynamics. We work out explicitly the case of a chaotic classical counterpart, for which we find semiclassical expressions for the value and the range of the plateau of fidelity. After the plateau ends, we find explicit expressions for the asymptotic decay, which can be exponential or Gaussian depending on the ratio of the Heisenberg time to the decay time. Arbitrary initial states can be considered; e.g., we discuss coherent states and random states.