量子力学中的密度矩阵与具有相同密度矩阵的系综的可区分性

讨论了密度矩阵的不同定义。建议使用完全密度矩阵、压缩密度矩阵和约化密度矩阵分别描写一个封闭量子体系的、一个系综中平均分子的和一个复合体系中的一个子系统的密度矩阵。强调这与现在人们认为的具有相同压缩密度矩阵的系综是完全等价的结论完全不同,具有相同压缩密度矩阵但是成分不同的系综可以通过系综整体测量来区别。作为一个应用,现在认为现有的核磁共振量子计算中没有纠缠的结论是没有根据的。Density matrix is one important tool in quantum mechanics, and it has very broad applications. However there are different definitions about the density matrix, and they describe quite different systems. There has been some misunderstanding about the density matrix in the community, and these misunderstandings hinder the right application of the density matrix. In this article, we discuss the different definitions of density matrix. We suggest to use the full density matrix, compressed density matrix and the reduced density matrix to describe the state of a complete quantum system, the state of an averaged particle in an ensemble and the state of part of a composite system. We stress that contrary to the wide accepted understanding that ensembles with the same compressed density matrix are physically indistinguishable, they are distinguishable through the so-called ensemble measurement. As an application, we suggest that the present conclusion that the present-day nuclear magnetic resonance quantum computation does not have quantum entanglement is groundless.     

量子达尔文主义

<正>量子力学的叠加原理要求量子态的任意组合也是合法的量子态。这和经验有些抵触:我们从来未见过既烤熟又鲜活的鸡。为什么不能按照薛定谔的方案烤鸡呢?答案是同环境间的相互作用协助选择了系统的择优状态。因为无法跟踪复合的系统—环境的每一个变量,人们只好依赖约化密度矩阵。约化密度矩阵是对环境求平均得到的;玻恩     

应用约化密度保真度确定自旋为1的一维量子Blume—Capel模型的基态相图

约化密度保真度（reducedensityfidelity）可以用来描述量子多体系统的量子相变,其是两个约化密度矩阵距离的度量．本文应用MERA（multi—scaleentanglementreorganizationansatz）算法,模拟自旋为1的一维量子Blume-Capel模型,并通过对约化密度保真度的计算,确定出其基态相图．单点和两点约化密度矩阵所包含的至关重要的信息的量是不同的,其会体现在约化密度保真度上．另外,本文还从局域序参量和系统能隙的角度,来探讨量子多体系统的相变．     

量子纠缠和贝尔不等式及其在量子信息处理中的应用

1964年,爱尔兰数学家约翰·贝尔(John Bell)根据隐变量理论推导出了2个粒子系统的测量结果应该满足的不等式关系和所涉及的测量基本逻辑.法国科学家阿兰·阿斯佩(Alain Aspect)、美国科学家约翰·克劳泽(John Clauser)和奥地利科学家安东·蔡林格(Anton Zeilinger)分别从实验上证伪了该不等式.贝尔不等式的证伪宣告了隐变量理论的终结,展示了量子纠缠的奇特性质.为表彰他们在“纠缠光子实验、验证违反贝尔不等式和开创量子信息科学”方面所做出的贡献,瑞典皇家科学院将2022年诺贝尔物理学奖授予这3位科学家.本文概述了量子纠缠的概念和贝尔不等式的推导,介绍了2022年诺贝尔物理学奖获得者的代表性研究工作,并展示了量子技术的可能应用.     

关于量子态可分性的O-约化判据

文章提出了一类纠缠目击者.它们是以局域正交可观测量的形式给出的,因而自动提供了利用局域测量和经典通信来探测纠缠的方法.利用Jamiokowski同构得到了相应的非完全正的正映射,从而导出一类新的可分性判据——O-约化判据.约化判据和重排判据都是该判据的特例.另外,还发现O-约化判据可以通过测量局域正交可观测量的一个厄米关联矩阵来获得物理的实现.作为应用,构造了Horodecki在1997年发现的第一个束缚纠缠态的纠缠目击者的清晰形式,并且提出了一类dd束缚纠缠态,其纠缠可以通过对局域正交可观测量进行置换来探测.     

关于量子态可分性的O-约化判据

文章提出了一类纠缠目击者.它们是以局域正交可观测量的形式给出的,因而自动提供了利用局域测量和经典通信来探测纠缠的方法.利用JamioΙkowski同构得到了相应的非完全正的正映射,从而导出一类新的可分性判据———O-约化判据.约化判据和重排判据都是该判据的特例.另外,还发现O-约化判据可以通过测量局域正交可观测量的一个厄米关联矩阵来获得物理的实现.作为应用,构造了Horodecki在1997年发现的第一个束缚纠缠态的纠缠目击者的清晰形式,并且提出了一类d d束缚纠缠态,其纠缠可以通过对局域正交可观测量进行置换来探测.     

Tb^3＋离子的能级之间约化矩阵元计算

本文利用中间耦合波函数,系统计算了Tb~(3 )离子的22个壮态之间U~K张量的约化矩阵元,为基础理论研究提供基本数据。     

Bell态原子与双模纠缠相干光场双光子相互作用系统的量子纠缠

运用全量子理论和数值计算的方法,借助于原子的量子约化熵研究了初始处于Bell态|β00>和| β10>的两原子与双模纠缠相干光场双光子相互作用系统中两原子与双模光场之间纠缠的演化特性.分析了光场强度、光场纠缠度及原子间相互作用强度对原子熵演化特性的影响.结果表明:随着双模光场的平均光子数的增大,原子熵的时间演化曲线逐渐变为规则振荡;增大原子间的相互作用强度,原子熵的振荡频率和振幅都减小;改变双模光场的纠缠度,原子熵的振荡频率和振幅都不发生改变.     

两量子比特与谐振子相耦合系统中的量子纠缠演化特性

在非旋波近似下, 利用相干态正交化展开方法, 对两量子比特与谐振子相耦合系统中的量子纠缠演化特性进行了精确计算. 讨论了在共振时, 两量子比特和谐振子耦合系统基态的性质以及量子比特和谐振子之间的纠缠与量子比特-量子比特间的纠缠的不同. 结果表明: 当不考虑外场时, 量子比特-量子比特间的纠缠随着耦合强度的增大从1迅速地减小到零, 表明了量子比特-量子比特间的纠缠对耦合强度是非常敏感的; 而量子比特和谐振子之间的纠缠随着耦合强度的增大从零迅速地增大, 但不能达到理论上的最大值2; 当初始时刻两量子比特没有纠缠时, 在弱耦合强度下, 真空场不能导致纠缠的产生; 而强的耦合非旋波效应则可以导致纠缠的突然产生现象. 关键词： 相干态正交化展开 非旋波近似 量子纠缠     

内禀退相干下海森伯XY模型中的热纠缠性质及其相干调控

通过求解系统的Milburn方程,研究了内禀退相干下两比特海森伯XY模型中的热纠缠性质. 讨论了非均匀磁场、系统初始纠缠度、 两比特的相对相位对系统热纠缠的调控作用.结果表明:在系统一定的初始条件下, 磁场的引入能够大大提高两比特间的热纠缠 程度;在固有退相干存在的情况下,系统热纠缠强烈依赖于两个自旋比特的初始态, 通过控制两自旋比特的相对相位和振幅,可以 获得系统的稳定热纠缠.结果还表明:在没有外界磁场时,发现Bell正交态是系统的"暗态", 它的热纠缠度在演化过程中不受系 统内禀退相干的影响.     

量子计算机原理及问题

讨论了量子计算机的原理及特色,着重介绍了实现它所遇到的问题及解决办法。     

Photonic quantum information processing

Information processing with light is ubiquitous, from communication, metrology and imaging to computing. When we consider light as a quantum mechanical object, new ways of information processing become possible. In this review I give an overview of how quantum information processing can be implemented with single photons, and what hurdles still need to be overcome to implement the various applications in practice. I will place special emphasis on the quantum mechanical properties of light that make it different from classical light, and how these properties relate to quantum information processing tasks.     

Nuclear-induced time evolution of entanglement of two-electron spins in anisotropically coupled quantum dot

We study the time evolution of entanglement of two spins in an anisotropically coupled quantum dot interacting with the unpolarised nuclear spins environment. We assume that the exchange coupling strength in the z direction J _z is different from the lateral one J _l . We observe that the entanglement decays as a result of the coupling to the nuclear environment and reaches a saturation value, which depends on the value of the exchange interaction difference J = ‖J _l ? J _z ‖ between the two spins and the strength of the applied external magnetic field. We find that the entanglement exhibits a critical behaviour controlled by the competition between the exchange interaction J and the external magnetic field. The entanglement shows a quasi-symmetric behaviour above and below a critical value of the exchange interaction. It becomes more symmetric as the external magnetic field increases. The entanglement reaches a large saturation value, close to unity, when the exchange interaction is far above or below its critical value and a small one as it closely approaches the critical value. Furthermore, we find that the decay rate profile of entanglement is linear when the exchange interaction is much higher or lower than the critical value but converts to a power law and finally to a Gaussian as the critical value is approached from both directions. The dynamics of entanglement is found to be independent of the exchange interaction for an isotropically coupled quantum dot.     

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.     

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     

Nonlocal advantage of quantum coherence and entanglement of two spins under intrinsic decoherence

We investigate the nonlocal advantage of quantum coherence(NAQC) and entanglement for two spins coupled via the Heisenberg interaction and under the intrinsic decoherence. Solutions of this decoherence model for the initial spin-1/2 and spin-1 maximally entangled states are obtained, based on which we calculate the NAQC and entanglement. In the weak region of magnetic field, the NAQC behaves as a damped oscillation with the time evolves, while the entanglement decays exponentially(behaves as a damped oscillation) for the spin-1/2(spin-1) case. Moreover, the decay of both the NAQC and entanglement can be suppressed significantly by tuning the magnetic field and anisotropy of the spin interaction to some decoherence-rate-determined optimal values.     

Entanglement diversion and quantum teleportation of entangled coherent states

The proposals on entanglement diversion and quantum teleportation of entangled coherent states are presented.In these proposals, the entanglement between two coherent states, $|\alpha\rangle$ and $|-\alpha\rangle$, with the same amplitude but a phase difference of $\pi$ is utilized as a quantum channel. The processes of the entanglement diversion and the teleportation are achieved by using the 50/50 symmetric beam splitters, the phase shifters and the photodetectors with the help of classical information.