【作者】 张国清；

【导师】 许晶波；

【作者基本信息】 浙江大学 ， 理论物理， 2019， 博士

【摘要】 量子信息学是一门以量子力学交叉信息科学发展而来的新兴学科。以量子力学作为理论基础,使得量子信息理论有着很多比经典信息理论优越的性质,尤其是在信息搜索和通信安全方面。当下正是前所未有的信息时代,互联网、大数据和人工智能等的高速发展依赖于信息处理速度和传播安全,而经典信息理论在这种日新月异的环境下越发显得捉襟见肘,正是量子信息理论的发展给了未来更多的可能。基于量子快速傅立叶变换的各种量子算法使得信息搜索和大数分解任务能够大幅突破经典算法的局限,而量子态不可克隆则给予量子密钥分发和保密通信理论上真正的安全。这门年轻的学科已然成为下一代计算机系统最坚实的理论基础,引起人们的广泛关注,寄托了人类对未来美好的憧憬。同时,量子信息学也为物理学的其他分支注入新的血液,例如量子信息的理论和实验促使了光学和原子分子物理的发展也为凝聚态物理等学科提供新的研究思路和方法。量子信息与经典信息的不同来自于量子系统的非经典关联,即量子关联,这也是实现各种量子信息任务不可或缺的资源。量子纠缠、量子谐错以及量子相干等量子关联被普遍认为是量子信息任务所需的物理资源而受到广泛的关注和研究。一方面,量子关联使得即使抛开传统的序参量和对称性破缺也能够研究量子相变和临界行为而成为凝聚态物理中一个研究热点。近年来,很多量子信息中的物理量,例如迹距离、保真度、量子纠缠和量子相干等都成功刻画了多体系统中的量子相变和临界行为。另一方面,量子关联作为物理资源是很脆弱的,周围环境噪声会诱发退相干而破坏量子关联,这也是实现量子计算必须要克服的障碍之一。因此,研究开放系统中量子关联的动力学规律和调控环境噪声的退相干对量子关联的影响就显得尤为必要。在本篇论文中,我们首先应用重整化群方法来研究多体系统的量子关联和量子相变问题。我们用实空间重整化群方法研究了具有Dzyaloshinskii-Moriya(DM)相互作用的XY自旋链中的相对熵相干性和Bell不等式破坏,发现相对熵相干性和Bell不等式破坏的一阶导数在量子相变点附近具有奇异性。通过对不同尺寸系统的重整化分析,发现在量子相变点附近重整化后的相对熵相干性和Bell不等式破坏满足一系列有限尺度线性行为并且服从普适的标度率。这些标度率的指数和量子相变区域的关联长度指数有着直接的关联。接着,我们利用密度矩阵重整化群(DMRG)方法研究了多体纠缠在各向异性XYZ自旋链量子相变点附近的行为,包括最近相邻相互作用的各向异性XYZ自旋链和次近相邻相互作用的各向异性XYZ自旋链。研究发现多体纠缠在所研究模型的量子相变点附近会剧烈变化并且剩余对全部纠缠比会在相变点达到最大值。结果表明不论是多体纠缠本身还是剩余对全部纠缠比都可以作为探测该模型量子相变的物理量。同时我们还发现次近邻相互作用强度和发生量子相变时的横向磁场强度之间存在一个线性关系,这个关系可以同时通过多体纠缠和相对熵相干性观察到。本篇论文的另一个重点是研究量子关联的动力学性质。我们结合矩阵积态和含时变分原理研究了无限长度相互作用Ising自旋链中纠缠产生、退相干过程与动态量子相变之间的关系。利用多体纠缠和相对熵相干性随时间演化的行为,我们发现在动态量子相变发生的区域内多体纠缠快速增加的同时相对熵相干性则是到达它的局域最小值,这意味着纠缠的产生得到加速和相干性得到回复这两个现象是可以同时出现在动态量子相变区域的。进一步,我们揭示了退相干和纠缠产生与横向磁场强度之间存在幂定理关系。退相干和纠缠产生的这个动力学特性可用于制备高相干强纠缠态,为复杂量子任务提供可能性。另一方面,我们利用级联动力学方程研究了玻色环境中具有量子记忆辅助的熵的不确定度和量子速度极限的动力学行为。发现弱测量可以在系统含时演化过程中压制熵的不确定度而不同弱测量强度下的量子速度极限则会有个周期性的交错,这种交错现象会因系统耦合强度增加而消失。弱测量压制系统含时演化过程中熵的不确定度这一现象同时也在有限温度玻色环境中观察到。我们还考虑了旋转波项的作用并且发现旋转波近似对于量子速度极限的研究是一个合适的近似而对于有量子记忆辅助的熵的不确定度的研究则不适用。更多还原

【Abstract】 Quantum information science is an an interdisciplinary research area which evolves quan-turn mechanics and information science.Quantum information theory has many advantages over classical information theory because of the quantum mechanics,especially in information search and communication security.In such an unprecedented information age,the rapid development of the Internet,big data and artificial intelligence are all depending on the speed of information processing and the security of information exchange.Classical information theory is becoming more and more stretched in this conditions.It is the development of quantum information the-ory which gives the future of information science more possibilities.Various quantum algorithms based on quantum fast Fourier transform greatly break through the limitations of classical algo-rithms in information search and large number decomposition tasks,while no-cloning theorem of quantum states gives quantum key distribution and secure communication the absolute security theoretically.This young area is considered to be the foundation for the next generation of com-puter systems,and has attracted widespread attentions.At the same time,quantum information science also injects new blood into other branches of physics.Experiments of quantum informa-tion motivate the development of optics and atomic physics,while theories of quantum information provide new research ideas and methods for the condensed-matter physics.The difference between quantum information and classical information comes from the non-classical correlation of quan-turn systems,that is,quantum correlation,which is an indispensable resource for realizing various quantum information tasks.Quantum entanglement,quantum discord,and quantum coherence are regarded as the physical resources required for quantum information tasks and have received numerous researches.On the one hand,quantum correlations make it possible to study quantum phase transitions and critical behaviors regardless of the traditional order parameters and symme-try broken,and thus become a research hotspot in the condensed-matter physics.In recent years,many physical quantities from quantum information science,such as trace distance,fidelity,quan-turn entanglement,and quantum coherence,have successfully been used to characterize quantum phase transitions and critical behaviors in many-body systems.On the other hand,quantum corre-lations are very fragile and easily destroyed by decoherent phenomenon induced from environment noise.This is one of the obstacles that must be overcome to achieve the real world quantum com-puting.Therefore,the study of quantum correlations and control of environmental decoherence in the dynamics of open quantum systems are of practical significance.In this paper,we first apply the renormalization group method to study the quantum cor-relations and quantum phase transitions in many-body systems.We make use of the real space renormalization group method to study the relative entropy of coherence and violation of Bell in-equality in the XY spin chain with Dzyaloshinskii-Moriya(DM)interaction and find that the first derivatives of the renormalized quantum coherence as well as Bell inequality exhibit singularity near the critical point of the quantum phase transition.We explore the finite-size scaling behav-iors of the first derivatives of the quantum coherence at the critical point of the quantum phase transition,and obtain several universal finite-size scaling laws.The critical exponents of these universal finite-size scaling laws are directly related to the correlation length exponent around the critical region.Next,we use the density matrix renormalization group(DMRG)method to study the behavior of multipartite entanglement near the quantum phase transition point of the anisotropic XYZ spin chain,including the anisotropic XYZ with nearest-neighbor interaction and next-nearest-neighbor interaction.Multipartite entanglement changes dramatically near the critical region and the residual-to-global entanglement ratio reaches its maximum at the critical point of the quantum phase transition.These results indicate that multipartite entanglement as well as the residual-to-global entanglement ratio can serve as good indicators to detect a quantum phase transition in this model.We also demonstrate a linear relation between the next-nearest-neighbor interaction strength and the critical magnetic field for an XYZ spin chain by using multipartite entanglement and quantum coherence.Another topic of this paper is to study the dynamical properties of quantum correlations.We study the decoherence procedure and entanglement generation for infinitely connected Ising chain in the dynamical quantum phase transition region by making use of the matrix-product state alone with the time-dependent variational principle.By calculating the evolution of multipartite entan-glement and relative entropy of coherence,we find that the quantum coherence reaches its local minimum near the critical time of the dynamical quantum phase transition while the multipartite entanglement increases steeply,which means the system undergoes a recovery of coherence as well as an acceleration of creating entanglement at the same time in the vicinity of a dynamical quantum phase transition.Furthermore,we investigate the depends of decoherence and entangle-ment generation on the strength of the transverse magnetic field and obtain several power-law rela-tions.These dynamical properties are important and useful in the preparation of highly-entangled states with strong coherence which may provide the possibility of completing complex quantum tasks.On the other hand,we use the hierarchical equations of motion method to study the dynamic behaviors of quantum memory-assisted entropy uncertainty relation and quantum speed limit in a quantum dissipative system.It is demonstrated that the weak measurement and measurement reversal can suppress the entropic uncertainty during the evolution of the system,and we find a periodical crossover of the quantum speed limit time for different weak measurement strengths,which disappears when increasing the coupling strength.Similar influence of the weak measure-ment on uncertainty relations is then explored at the finite temperature.We also consider the effect of the counter-rotating-wave term and show that the rotating-wave approximation is an applicable approximation when studying quantum speed limit time but not appropriate when investigating the quantum-memory-assisted entropic uncertainty relation.更多还原