高维开放量子系统的非马尔科夫动力学研究

发布时间：2018-11-24 17:13

【摘要】：近些年,在开放量子系统中广泛存在的非马尔科夫动力学已经吸引了研究人员广泛的关注。通俗地讲,量子非马尔科夫动力学过程实质上就是开放系统流向环境的信息重新流回系统的过程。而在信息重新流回系统的过程中,将会导致纠缠和量子迹距离等一些关键的物理量出现振荡。开放量子系统非马尔科夫动力学的研究所涉及的内容是相当广泛的。在之前,大多数关于非马尔科夫动力学的研究都主要局限于二能级系统,而关于高维度量子系统的研究却很少涉及。然而,高维开放系统和二能级系统一样也是大量存在于自然之中,使用高维量子系统编码还能提升量子密码学的安全性,并且在量子容错计算和量子纠错中高维量子系统相较于二能级系统有无法比拟的优势。本文主要研究几种典型的高维开放量子系统的非马尔科夫动力学。在第一章中,我们主要介绍了关于量子信息、开放量子系统和量子退相干的一些基础知识,包括量子迹距离、量子纠缠及其度量、量子动力学映射、量子可分性、马尔科夫主方程及非马尔科夫主方程、三种典型的量子退相干通道等。在第二章中,我们主要介绍了四种相当典型的关于量子非马尔科夫性的度量方式。第一种为基于量子迹距离的度量方式,第二种为基于量子纠缠的度量方式,第三种为基于量子关联的度量方式,第四种为基于量子可分性的度量方式。第三章,提出了一种精确求解和零温波色环境相互作用的多能级V型原子非马尔科夫动力学的方法。特别关注了三能级V型原子的纠缠演化及其非马尔科夫性。发现相较于非共振区域,在共振区域内纠缠衰减得更快且非马尔科夫性更弱。更为重要的是,本章展示了由不同传输通道所造成的非马尔科夫性的干涉现象,并指出了干涉相长区域和干涉相消区域。第四章,主要研究了处于退相位环境中的自旋S系统的纠缠演化和非马尔科夫动力学。精确的解析表达式表明退相干函数支配着自旋S系统动力学过程中的相干性演化、纠缠演化和非马尔科夫性。对于欧姆热库和亚欧姆热库,纠缠随时间单调的衰减,相应的动力学过程为马尔科夫过程。而对于超欧姆热库而言,由于退相干函数是振荡的,导致纠缠出现复苏现象,相应的动力学过程为非马尔科夫过程。在本章末尾,还探讨了非马尔科夫性和系统维度之间的关系。在第五章中,我们对本文的工作进行了一个简短的总结与展望。
[Abstract]:In recent years, non-Markov dynamics, which widely exist in open quantum systems, have attracted much attention. In general, the quantum non-Markov dynamics process is essentially an open system flow to the environment of the information reflow back to the system process. In the process of information reflow back system, some key physical quantities, such as entanglement and quantum trace distance, will oscillate. The study of non-Markov dynamics of open quantum systems is quite extensive. Previously, most studies on non-Markov dynamics were mainly confined to two-level systems, but the studies of high-dimensional quantum systems were rarely involved. However, high dimensional open systems, like two-level systems, are abundant in nature, and the use of high-dimensional quantum system coding can also enhance the security of quantum cryptography. Moreover, in quantum fault-tolerant computation and quantum error correction, high-dimensional quantum systems have incomparable advantages over two-level systems. In this paper, the non-Markov dynamics of several typical high-dimensional open quantum systems are studied. In the first chapter, we mainly introduce some basic knowledge about quantum information, open quantum system and quantum decoherence, including quantum trace distance, quantum entanglement and its measurement, quantum dynamic mapping, quantum separability. Markov master equation and non-Markov master equation, three typical quantum decoherence channels, etc. In the second chapter, we mainly introduce four typical measures of quantum non-Markov property. The first is based on quantum trace distance, the second is based on quantum entanglement, the third is based on quantum correlation, and the fourth is based on quantum separability. In chapter 3, a method for solving the non-Markov dynamics of multi-level V-type atoms with zero temperature wave color environment is presented. Special attention is paid to the entanglement evolution of three-level V-type atoms and their non-Markov properties. It is found that entanglement in the resonance region attenuates faster and the non-Markov property is weaker than that in the non-resonant region. More importantly, this chapter shows the non-Markov interference caused by different transmission channels, and points out the long interference region and interference cancellation region. In chapter 4, the entanglement evolution and non-Markov dynamics of spin S system in dephase environment are studied. The exact analytical expression shows that the decoherence function dominates the coherence evolution, entanglement evolution and non-Markov property in the dynamics of the spin S system. For ohmic heat reservoirs and YAOM heat reservoirs, the entanglement decays monotonously with time, and the corresponding dynamical processes are Markov processes. For the super-ohmic heat reservoir, the decoherence function is oscillating, which leads to the recovery of entanglement, and the corresponding dynamic process is a non-Markov process. At the end of this chapter, the relationship between non-Markov property and system dimension is also discussed. In the fifth chapter, we give a brief summary and prospect of this paper.
【学位授予单位】：湖南师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O413

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