广义量子主方程:教程综述和最新进展（英文）

广义量子主方程(GQME)为模拟嵌入在量子环境中的开放量子体系的约化动力学提供了一种通用且严格的计算方法.开放量子体系的动力学在能量、电荷以及量子相干转移过程和光化学反应中至关重要.量子系统通常被定义为我们感兴趣的自由度,例如捕光分子的电子态或凝聚态体系中的特定振动模式.系统周围的环境也被称为热浴,必须考虑它对系统的影响.例如,广义量子主方程理论中用投影算符方法对其进行描述.本综述总结了广义量子主方程的两种标准形式,即时间卷积形式的Nakajima-Zwanzig GQME和无卷积形式的广义量子主方程.在更流行的NZ-GQME形式中,记忆核刻画了非马尔可夫和非微扰效应,给出了约化密度矩阵的精确量子动力学.总结了几种通过含有分子信息但无投影算符的时间关联函数作为输入信息,进而求解含投影算符的记忆核的方法.特别值得一提的是近期提出的NZ-GQME改进版方法,该方法是基于将哈密顿量划分为更通用的对角和非对角部分.上述系统相关的热浴时间关联函数可以通过数值精确或近似量子动力学方法计算.本文将有助于理解广义量子主方程的理论背景,并且展望通过GQME与量子计算技术的结合解决使用当今最先进的经典超级计算机无法解决的与量子动力学和量子信息相关的复杂问题.     

时间无卷积广义主方程中核函数的精确解和高阶微扰展开:在自旋-玻色模型和激发态能量转移中的应用（英文）

时间无卷积量子主方程是量子系统与热库耦合的约化动力学模拟的重要工具.时间无卷积主方程的核心是核函数(或产生函数),它描述了热库自由度的作用.由于时间无卷积主方程中核函数的精确值通常很难解析求解,实际应用时间无卷积主方程时多采用二阶或四阶微扰法对其进行求解.本文利用级联方程及其拓展方程,提出了一种计算时间无卷积主方程核函数精确值和高阶微扰展开的新方法,并将该方法应用到不同参数下的自旋-玻色模型中,测试了核函数高阶展开的收敛性.此外,本文还讨论了在自旋-玻色模型中以及FennaMatthews-Olson复合物激发态能量转移中核函数的精确解出现奇异性的情况.     

耗散子运动方程与福克-普朗克量子主方程

发展非线性耦合环境下精确、非微扰的量子耗散方法仍然是一个巨大的挑战.本文针对线性和二次耦合热浴模型,介绍了两种刻画系统与环境耦合动力学的有效方法.一个是耗散子运动方程（DEOM）理论,最近已被扩展到处理非线性耦合环境.另一个是推广的福克-普朗克量子主方程（FP-QME）方法,将在这项工作中基于DEOM推导给出.本文对这两种方法进行了详细的比较,并重点介绍了所涉及的准粒子图像、物理含义以及实现方案.     

随机薛定谔级联方程：理论和应用

随机薛定谔级联方程是一种基于波函数的严格量子动力学方法，它可用于研究耦合到玻色子热库的复杂体系中的量子动力学过程. 本综述从开放量子体系费曼路径积分的影响泛函出发，概述了随机薛定谔级联方程的一般理论框架和各种具体表述形式，并通过对复杂体系中超快激发能量转移过程的模拟来展示方法的应用范例和计算效率.     

耦合系统的主方程(Ⅰ)

本文运用与时间有关的投影算符,推导出广义耦合主方程,并在第一级玻恩近似下,推出 N 个任意子系的只含对角元部分的耦合主方程.     

量子点腔系统中抽运诱导受激辐射与非谐振腔量子电动力学特性的研究

从量子点和腔相互作用的哈密顿量出发,利用包括非相干抽运,退相干项主方程,并结合量子回归定理,考虑相关初始条件,理论推导和数值计算相结合得出量子点多光子发射光谱精确数值结果.分析多光子发射光谱(费米子统计)和相应单光子情况(玻色子统计)时,得到依据费米子统计,退相干和热浴模型的多光子发射光谱同最近文献[22]量子点——微柱腔实验结果符合得非常好.结合理论和当前实验,显示了量子点腔系统中抽运诱导受激辐射和非谐振腔量子电动力学. 关键词： 量子点 微腔 受激辐射 发射光谱     

量子凝聚体的量子关联与微分散射截面之间的关系

研究量子系统的量子关联和导致量子关联形成的基本的动力学过程.讨论凝聚的出现与非对角长程序的形成的相互联系.讨论作为显示这样一个序的一个初级表示形式的单粒子密度矩阵.并在最低阶导出直接和反转过程的散射截面的一个表示.由此,关于量子关联的重要信息能够直接地从这些过程的微分散射截面导出.     

费米型级联运动方程的绝热截断方案

研究开放量子系统的量子耗散动力学对于理解许多新奇量子现象背后的机制和实现量子器件的精确量子态控制具有重要意义. 级联运动方程方法已成为研究这类量子耗散动力学最常用的数值方法之一. 然而，在处理强电子关联系统时，准确描述强关联效应需要高的级联截断层数. 这导致级联运动方程方法需要耗费大量物理内存和计算时间. 为了解决该问题，将具有最快耗散速率的耗散模式与其他较慢的耗散模式分离，提出了一种级联运动方程的绝热截断方案. 在单杂质安德森模型上进行的数值测试表明，与传统的方案相比，该截断方案显著地降低了级联运动方程收敛需要的截断层数. 此外，该截断方案缓解了长时间耗散动力学中的数值不稳定性.     

杨-巴克斯特自旋1/2链模型的量子关联研究

量子系统各部分间的量子关联可以作为量子信息应用研究的基础资源. 而量子失协是度量量子关联大小的物理量. 由此研究杨-巴克斯特自旋1/2链模型的量子关联情况. 首先利用两个杨-巴克斯特方程的解得到相应的杨-巴克斯特自旋1/2链模型. 然后, 计算分析热平衡时杨-巴克斯特自旋1/2链模型的量子失协、几何量子失协和量子纠缠随着温度和外磁场的变化情况. 结果表明对于杨-巴克斯特自旋1/2链模型, 量子失协和几何量子失协能够比量子纠缠更好地度量量子关联.     

强关联电子体系的量子蒙特卡罗计算

理解强关联电子体系是一个长期的重要目标,该体系的魅力不仅在于其背后蕴藏着深刻的物理,还在于其中涌现出的丰富物质态在量子调控、量子计算等领域具有巨大的潜在应用价值.同时,理论上非微扰地理解强关联电子体系是极其困难的,一直充满挑战.量子蒙特卡罗计算是一类非微扰计算的标准方法,有助于对强关联电子体系提供非微扰的理解,因而广泛运用于凝聚态和高能物理领域.然而,量子蒙特卡罗计算通常会受到负符号问题的困扰.本文将具体介绍一些无负符号关联电子模型的设计思路,并讨论我们近期提出的符号边界理论.通过设计无负符号或者具有代数符号行为的强关联电子模型,可以帮助人们研究很多重要的量子多体问题,包括巡游磁性量子临界行为、非常规超导和磁性序的竞争,以及莫尔(moiré)量子物质中的关联物相与相变等.     

Polarized soliton pulses generation using nonlinear micro ring resonators for multi- and long distance links

We propose a new concept of quantum soliton pulses generation using a soliton pulse in the micro ring resonators. Firstly, the chaotic soliton pulses are generated and circulated within the integrated micro ring resonators. Secondly, the specific second harmonic pulses are selected by using the appropriate ring parameters. The superposition of the second harmonic pulses within the micro ring devices introduces the randomly polarized photons within the micro ring device. The entangled photon visibility of the polarized photon is seen after passing the polarization control devices and projecting on the detectors. The optimum entangled photon visibility is obtained. The advantage of such a system is that the quantum repeater unit can be redundant for long distance quantum communication link, whereas the use of the system for multi-entangled photon sources and links is also available. The system degradation via the entangled photon states timing walk-off is also discussed.     

A cross-disciplinary introduction to quantum annealing-based algorithms

A central goal in quantum computing is the development of quantum hardware and quantum algorithms in order to analyse challenging scientific and engineering problems. Research in quantum computation involves contributions from both physics and computer science; hence this article presents a concise introduction to basic concepts from both fields that are used in annealing-based quantum computation, an alternative to the more familiar quantum gate model. We introduce some concepts from computer science required to define difficult computational problems and to realise the potential relevance of quantum algorithms to find novel solutions to those problems. We introduce the structure of quantum annealing-based algorithms as well as two examples of this kind of algorithms for solving instances of the max-SAT and Minimum Multicut problems. An overview of the quantum annealing systems manufactured by D-Wave Systems is also presented.     

Quantum correlation dynamics in photosynthetic processes assisted by molecular vibrations

During the long course of evolution, nature has learnt how to exploit quantum effects. In fact, recent experiments reveal the existence of quantum processes whose coherence extends over unexpectedly long time and space ranges. In particular, photosynthetic processes in light-harvesting complexes display a typical oscillatory dynamics ascribed to quantum coherence. Here, we consider the simple model where a dimer made of two chromophores is strongly coupled with a quasi-resonant vibrational mode. We observe the occurrence of wide oscillations of genuine quantum correlations, between electronic excitations and the environment, represented by vibrational bosonic modes. Such a quantum dynamics has been unveiled through the calculation of the negativity of entanglement and the discord, indicators widely used in quantum information for quantifying the resources needed to realize quantum technologies. We also discuss the possibility of approximating additional weakly-coupled off-resonant vibrational modes, simulating the disturbances induced by the rest of the environment, by a single vibrational mode. Within this approximation, one can show that the off-resonant bath behaves like a classical source of noise.     

On “Arbitrated quantum signature of classical messages against collective amplitude damping noise”

This study points out that a dishonest party in Yang and Wen's arbitrated quantum signature scheme [Opt. Comm. 283, (2010) 3198-3201] can reveal the other party's secret key without being detected by using the Trojan-horse attacks. Accordingly, the security requirements of a quantum signature, i.e. unforgeability and undeniability, may not be satisfied in their scheme.     

Quantum information capsule in multiple-qudit systems and continuous-variable systems

Quantum correlations in an entangled many-body system are capable of storing information. Even when the information is injected by a local unitary operation to the system, the entanglement delocalizes it. In a recent study on multiple-qubit systems, it is shown that a virtual qubit defined in the correlation space plays a role of perfect storage of delocalized information, which is called a quantum information capsule (QIC). To enhance the capacity of quantum information storage, it is crucial to formulate the cases for multiple-qudit systems and continuous-variable (CV) systems. We analytically prove that it is possible to construct a QIC for general write operations of the systems. It turns out that the extension to quantum field theory is achievable. For Gaussian states, we explicitly construct a QIC for shift write operations. We analyze the time-evolution of QIC in a CV system to demonstrate the diffusion of information in entangled pure states.     

Impact of quantum–classical correspondence on entanglement enhancement by single-mode squeezing

Quantum entanglement between two field modes can be achieved through the collective squeezing of the two respective modes. If single-mode squeezing is performed prior to such a two-mode squeezing, an enhancement of entanglement production can happen. Interestingly, the occurrence of this enhancement can be implicitly linked to the local classical dynamical behavior via the paradigm of quantum–classical correspondence. In particular, the entanglement generated through quantum chaos is found to be hardly enhanced by prior squeezing, since it is bounded by the saturation value of the maximally entangled Schmidt state with fixed energy. These results illustrate that entanglement enhancement via initial squeezing can serve as a useful indicator of quantum chaotic behaviour.     

New arbitrated quantum signature of classical messages against collective amplitude damping noise

Recently, Chong et al. [Opt. Comm. 284, (2011) 893-895] pointed out that a dishonest party in Yang and Wen's arbitrated quantum signature scheme [Opt. Comm. 283, (2010) 3198-3201] is able to reveal the other party's secret key without being detected by using the Trojan-horse attacks. However, the solution to avoid the attack still remains open. This work further points out that in Yang and Wen's scheme, the arbitrator is unable to arbitrate the dispute between two users. Consequently, a user can deny that he/she has signed or verified a signature without performing a Trojan-horse attack. A solution is proposed to solve this problem as well as the open problem mentioned earlier.     

A careful estimation of photon rescatterig in atomic-cascade experimental tests of Bell's inequality

Summary In this paper we show that, in every atomic-cascade experiment performed up to now for testing Bell's inequality, the second photon of the atomic cascade undergoes rescattering with considerable probability. The only experiment of this type in which rescattering is negligible is the Holt and Pipkin's one, but this is also the only experiment whose results grossly violate quantum-mechanical predictions.

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Riassunto Nel presente lavoro si mostra che, in ogni esperimento con cascata atomica realizzato fino ad oggi per indagare la disuguaglianza di Bell, la probabilità che il secondo fotone della cascata atomica subisca rescattering è notevolumente alta. L'unico esperimento del tipo suddetto in cui il rescattering è trascurabile è quello di Holt e Pipkin, ma questo è anche l'unico esperimento i cui risultati sono in netto contrasto con le previsioni quantomeccaniche.

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Резюме В этой статье мы показываем, что в экспериментах по наблюдению атомных каскадов, вьшолненных для проверки неравенства Белла, второй фотон атомного каскада претерпевает перерассеяние с большой вероятностью. Единственный эксперимент этого типа, в котором процесс перерассеяния пренебрежимо мал, является эксперимент Хольта и Пипкина. Но указанный эксперимент, в свою очередь, является единственным экспериментом, результаты которого существенно противоречат предсказаниям квантовой межаники.

     

Properties of the translation matrix of spherical partial waves in LEED theory

Summary The properties of the matrix which allows the translation of the centre of the expansion in terms of spherical partial waves of a wave function are examined here. It is shown that the matrix can be decomposed in the product of commuting matrices relative to preassigned directions, for example the directions of the axes of the reference frame. Furthermore, an exponential form of that matrix is obtained. Work supported by C.N.R. and M.P.I.     

Eigenvalues and eigenvectors of the translation matrices of spherical waves of multiple-scattering theory

Summary The exponential nature of the translation matrixG of spherical free waves has been set forth in a previous paper. The explicit expression of the exponential form of the translation matrix is given here, once the eigenvectors and the eigenvalues ofG have been found. In addition, the eigenproblem relative to the matrix which transforms outgoing waves scattered by a centre in a set of spherical free waves centred at a different point is solved. Work supported by C.N.R. and M.P.I.