【作者】 陈琪；

【导师】 许晶波；

【作者基本信息】 浙江大学 ， 理论物理， 2020， 博士

【摘要】 量子信息学是一门将量子力学的物理原理应用到信息科学的研究当中的新兴交叉学科,它具有许多传统信息学所不具有的优势,从而能够让信息的传递更为安全,计算的效率更高。量子态测量坍塌原理和量子态不可克隆原理从物理原理上保证了量子信息学中信息传递的绝对安全,例如在量子密匙分发过程当中人们就能有效的探测到窃听者的存在,从而保障信息传递的安全性。当量子力学的基本原理被考虑到量子算法中时,就会发现计算效率会大大提高,例如信息搜索的量子Grover算法和整数的质数分解的量子Shor算法。其中量子Shor算法对整数的质数分解的突破甚至会让现在的许多保密技术不再安全,这无疑对现代社会的网络安全提出了挑战。不论是量子通信还是量子计算,其实都依赖于系统中的量子资源,而量子资源来源于系统中存在的各种各样的量子关联,例如量子纠缠、量子相干性和量子协错等等。这些量子资源在实现不同的量子任务中都有着成功的应用。现实中的量子系统通常会不可避免的和其周围的环境产生相互作用,这种相互作用会通过退相干效应降低甚至破坏系统中的量子关联,因此如何抑制量子系统的退相干效应并提升系统中的量子资源就成为了一个非常重要的研究方向。量子信息学的发展还对凝聚态物理中的量子相变的研究做出了贡献。传统的关于量子相变的研究要求序参量和对称性破缺的知识,但是寻找一个系统的序参量往往存在困难。通过利用量子信息学中的一些概念,量子相变的研究就会变得容易开展。在本论文中,我们探讨了如何利用量子信息学中的概念去研究多体系统的量子相变。首先利用了密度矩阵重整化群方法对一维拓展compass自旋系统进行了研究,并利用多体纠缠讨论了系统量子相变。发现多体纠缠可以很好的捕捉到系统量子相变的发生并且得到了多体纠缠在临界点附近的标度行为。接着还利用迹距离和量子相干性对一维拓展compass自旋系统的量子相变进行了研究,同样得到了准确的量子相变点和相应的标度行为。另外,我们还利用量子信息学的方法对二维Kitaev蜂巢模型的量子相变进行了研究。通过对二维Kitaev蜂巢模型的对称性分析,可以得到了其约化密度矩阵的形式,然后利用了量子Jensen-Shannon divergence平方根相干性对其量子相变进行了研究并得到了该模型在参数空间中的相图,量子Jensen-Shannon divergence平方根相干性的一阶导数能够很好的探测到量子相变的发生和其标度行为。然后还利用迹距离和相对熵相干性对二维Kitaev蜂巢模型的量子相变进行了研究,发现它们也都能很好的探测到量子相变的发生并具有良好的标度行为。另一方面还具体讨论了如何抑制量子系统中退相干效应从而提高系统的量子关联。由于退相干效应的存在,量子系统中的量子关联会降低甚至消失,这会直接导致各种量子任务的失败。本文主要讨论了基于量子跃迁的反馈方案和伴随量子测量反转的弱测量方案对里德堡原子系统的影响。通过研究发现,基于量子跃迁的反馈能够增加系统的相对熵相干性,这说明里德堡原子系统中的退相干效应在基于量子跃迁的反馈作用下被抑制了。我们还讨论了基于量子跃迁的反馈对系统占据数的影响,并发现基于量子跃迁的反馈可以降低系统的自发辐射效应,这可能是该方案能够抑制退相干效应的原因。还进一步讨论了基于量子跃迁的反馈对量子Jensen-Shannon divergence平方根相干性和系统的不确定关系的影响,并发现基于量子跃迁的反馈能够提高量子Jensen-Shannon divergence平方根相干性的值,并降低系统的不确定关系中的不确定界限。对于伴随量子测量反转的弱测量方案来说,发现它同样能够增加里德堡原子系统的相干性,降低系统的不确定度和不确定度界限以及增加量子纠缠。更多还原

【Abstract】 Quantum information science is an emerging interdisciplinary research area that has applied the principles of quantum mechanics into information science research,and it has many advantages over traditional information science,which allows for the more secure transfer of data and greater efficiency in computations during quantum information pro-cessing.The absolute security of information transmission is physically guaranteed by the quantum state collapse and the no-cloning theorem in quantum information science.For example,in quantum key distribution,it is very effective for detecting the presence of eavesdroppers and fundamentally guaranteeing the security of information transfers.Ad-ditionally,when the basic principles of quantum mechanics are considered in the design of quantum algorithms,a vast improvement in the efficiency of computation can be ob-tained,such as the quantum Grover algorithm and the quantum Shor algorithm which have been successfully applied in increasing information search capacity and the decompo sition of int,egers into their primes,respectively.The quantum Shor algorithm represents such a breakthrough in the prime numbers decomposition of integers that many current encryption technologies are rendered no longer secure,and this undoubtedly is a challenge for cyber security in modern societies.In fact,quantum communication and quantum com-puting both rely on the quantum resources in their systems,and these quantum resources originate from various kinds of quantum correlations within the system,including quantum entanglement,quantum coherence,quantum discord,quantum fidelity,and so on.These quantum resources have been successfully applied into different quantum tasks.In real physical environments,a quantum system will unavoidably generate interactions with its surrounding environment,and because of the existence of the quantum decoherence effect,these interactions may reduce or even destroy the quantum correlations within a system.Thus,how to suppress the quantum decoherence effect and increase the quantum resources of the system has become an important research direction.The development of quantum information science has also made contributions to the research into quantum phase tran-sitions in condensed matter physics.Traditional research into quantum phase transitions requires an understanding of order parameters and symmetry breaking.However,it is dif-ficult to obtain the order parameters of a system.Fortunately,by making use of some concepts from quantum information theory,research into quantum phase transitions can be conducted relatively easily.In this thesis,we discuss how to use concepts from quantum information science to study the quantum phase transitions of many-body systems.We first utilize the density matrix renormalization group method to solve a one-dimensional extended quantum com-pass spin model and use multipartite entanglement to study the quantum phase transitions of the system.We find that multipartite entanglement is a good measure for detecting the quantum phase transitions,and the scaling behaviors of the multipartite entanglement are also obtained nearby the critical point.We then use trace distance and quantum coherence to study the quantum phase transitions of the one-dimensional extended quantum com-pass spin model,and also obtain accurate critical points of the quantum phase transitions and their corresponding scaling behaviors.Furthermore,the quantum phase transitions of the two-dimensional Kitaev honeycomb model is studied by making use of the quantum information theory methods.Through symmetry analysis of the two-dimensional Kitaev honeycomb model,we obtain the reduced density matrix of the model,and then utilize the quantum coherence based on the square root of the quantum Jensen-Shannon divergence to study the quantum phase transitions,and obtain the phase diagrams of the model in parameter space.The first derivative of the quantum coherence based on the square root of the quantum Jensen-Shannon divergence can effectively detect the quantum phase transi-tions,and their corresponding scaling behaviors can also be obtained through calculations.Additionally,we also use trace distance and relative entropy coherence to study the quan-tum phase transitions of the two-dimensional Kitaev honeycomb model,and find that they are also good measures for detecting the quantum phase transitions.The scaling behaviors of trace distance and relative entropy coherence of the two-dimensional Kitaev honeycomb model are also examined.We also discuss how to suppress the quantum decoherence effect and increase quan-tum correlations in the quantum system.Because of the existence of quantum decoherence,quantum correlations in quantum systems decrease and even disappear entirely,and this leads to the failure of various kinds of quantum tasks.We mainly discuss the effects of quantum-jump-based feedback and weak measurement along with quantum measurement reversal on the Rydberg atoms systems.We find that the effect of quantum-jump-based feedback can enhance the relative entropy coherence of the system,which provides evidence that decoherence effect in Rydberg atoms systems can be suppressed by quantum-jump-based feedback.We also discuss the influence of the quantum-jump-based feedback on the occupation number of the system,and find that quantum-jump-based feedback can reduce the spontaneous radiation effect of the system.This may be the reason why this method can suppress the decoherence effect of the Rydberg atoms system.We then proceed to discuss the effect of quantum-jump-based feedback on the quantum coherence based on the square root of the quantum Jensen-Shannon divergence and the uncertainty relation of the system,and find that quantum-jump-based feedback can enhance the quantum coherence based on the square root of the quantum Jensen-Shannon divergence,and reduce the un-certainty bound of the system.We also find that weak measurement along with quantum measurement reversal can enhance the quantum coherence of the Rydberg atoms system,reduce the uncertainty and uncertainty bound of the system and enhance the quantum entanglement of the system.更多还原