【作者】 聂晶；

【导师】 衣学喜；

【作者基本信息】 大连理工大学 ， 理论物理， 2009， 博士

【摘要】 量子信息学是量子理论与信息学交叉而产生的新兴学科,它的出现给未来的科技发展带来了美好的前景。量子信息学的发展与完善离不开对量子纠缠和量子控制等相关问题的深入研究。本文就量子纠缠与量子控制的一些问题进行了理论探讨,并得到了一些有意义的结果。本文大体可分为四个部分。第一章和第二章构成本文的第一部分,第一章里较为系统的介绍了研究量子纠缠、量子控制的重要意义,以及目前的研究进展。第二章中我们介绍了与本文相关的量子信息学的基本知识。本文的第二部分由第三章和第四章构成,主要讨论了量子多体系统中量子纠缠与量子相变的关系。在第三章中,我们对狄克模型进行了简单的介绍,并研究了在具有偶极相互作用的狄克模型中子系统的纠缠性质,以及量子相变现象。研究表明,子系统间的纠缠性质可以很好的反应量子相变的发生,原子间的偶极相互作用对子系统间的纠缠有重要影响。在第四章里,我们介绍了XY自旋链,通过研究与自旋链耦合的中心粒子间的纠缠性质,讨论了自旋链环境相变及温度对中心粒子间纠缠的影响。我们的研究表明,中心粒子间的纠缠性质和系统的初态有着密切的联系。在自旋链温度接近绝对零度时,中心粒子间的纠缠能够反应自旋链的相变现象,当自旋链温度升高时,自旋链自身的量子相变现象被热力学涨落淹没,温度还会引发中心粒子出现退纠缠现象。第五章是本文的第三部分,在这一章里,我们研究了量子纠缠在量子信息里的一个重要应用——量子隐形传态,着重讨论了利用量子多体纠缠完成多量子比特的传送任务。通过一种矩阵符号,我们得到了一个描述量子隐形传态中量子通道和测量基之间关系的判据方程,并给出了方程的一些特解,这对寻找和利用多体系统纠缠资源实现多比特量子隐形传送具有一定的帮助。本文的第四部分是第六章,我们介绍了量子控制的基本概念,回顾了前人的一个非相干量子控制方案,在前人的工作基础之上,提出了一个新的非相干控制方案,这个方案不仅可实现两能级系统控制,并且可以成功实现对有限维量子系统的控制。文章的最后,给出了全文的总结和展望。更多还原

【Abstract】 Quantum information theory,a combination of quantum mechanics and information theory,is a brand-new subject,whose appearance brings about a bright future for the development of science and technology.And the development and improvement of quantum information is dependent on the profound research on quantum entanglement and quantum control.This dissertation mainly discusses some problems related to quantum entanglement and quantum control in theory,and obtains some important results.This dissertation consists of four parts.The first part includes Chapter 1 to Chapter 2.Chapter 1 introduces the significant meaning of quantum entanglement and quantum control systematically as well as their current studies.And the related theories to quantum information are presented in Chapter 2.Part two is composed of Chapter 3 and Chapter 4,which chiefly discusses the relationships between quantum entanglement and quantum phase transition in multi-particle system. Chapter 3 begins with brief introduction of the Dicke model,and then demonstrates the research on the entanglement properties between subsystems as well as quantum phase transition in the Dicke model with the dipole-dipole interactions.The results demonstrate that the entanglement properties between subsystems can well signal the occurrence of quantum phase transition,and the dipole-dipole interactions have a great impact on the entanglement between the subsystems.The XY spin chain is presented in Chapter 4,and the entanglement evolution of bipartite spin-1/2 system coupled to a common surrounding XY chain in transverse fields at nonzero temperature is studied.The results indicate that the properties of entanglement between central particles are closed associated with the initial state of the system.When the temperature of the system is near absolute zero,the entanglement between central particles can reflect the quantum phase transition in spin chain.As the temperature increases,the quantum phase transition is washed out by thermodynamical fluctuations.In addition,the temperature can lead to disentanglement between central particles.Chapter 5 alone consists of the third part,in which quantum teleportation,an important application of quantum entanglement in quantum information,is studied.And emphasis is placed on the study of multi-qubit teleportation by employing quantum multi-particle entanglement. By introducing matrix operator,the judgment equation reflecting the relationships between quantum channel and measurement basis in quantum teleportation is described and some special solutions of the equation is given,which can help to seek and use multi-particles entanglement recourses in order to realize the quantum teleportation.Chapter 6 is the fourth part,which presents the concepts of quantum control,and reviews a previous incoherent quantum control scheme.Based on the former scheme,a new scheme is put forward,which can not only realize the controlling of two-level quantum system,but also can be extended to control the finite-dimensional quantum system.Finally,the results are summarized and suggestions are given for future research work.更多还原