基于一些测量的可分性准则

发布时间：2018-03-27 22:34

本文选题：k-可分量子态　切入点：纠缠探测　出处：《河北师范大学》2016年博士论文

【摘要】：近年来,量子纠缠在量子信息处理方面的应用与日俱增,它作为一种新的物理资源备受关注.对量子纠缠的研究有重要的科学意义.复合量子系统中量子纠缠态的探测是量子纠缠理论中的基本问题之一.相互无偏基,相互无偏测量和广义对称信息完备测量是量子信息理论中相关的三个概念,我们用这三种测量对量子纠缠的探测进行了研究,得到了两体不同维量子系统,多体高维量子系统和多体多能级量子系统上的可分性准则.基于算子Δ,我们得到了新的可分性准则,并且证明了它们分别比之前相应的准则更有效.我们给出的多体多能级量子系统上的纠缠判据不限制子系统的维数相同,因此可以结合-可分的概念直接用来探测-不可分量子态.对于子系统维数差异较大的情况,根据维数之间的关系改进了判别准则,大大减少了被忽略的测量,提高了准则的效率.这些可分性准则比之前已知的准则更有效,应用范围更广,并且可以通过实验实现对未知量子态纠缠的探测.本文分为以下五章.第一章,我们回顾了一些纠缠的基本概念,相互无偏基,相互无偏测量和广义对称信息完备测量的概念及基于它们在量子纠缠探测方面的最新进展.第二章,我们基于三种测量研究两个子系统维数不同的复合量子系统上的纠缠探测,得到了更有效且应用范围更广的可分性准则.第三章,我们进一步将两体系统上的可分性准则推广到多体系统上得到了多体高维系统中.由于在可分性准则中没有限定子系统维数相同,因此我们的准则可以直接应用来探测固定划分上的-不可分量子态.这样我们不但可以探测给定的量子态是否纠缠,还可以一定程度上探测纠缠的程度.第四章,我们讨论了纠缠witness和可分性准则的关系,并给出由得到的可分性准则构造的纠缠witness.第五章,我们进行了总结和展望.
[Abstract]:In recent years, the application of quantum entanglement in quantum information processing is increasing. As a new physical resource, it is of great scientific significance to study quantum entanglement. The detection of quantum entangled states in composite quantum systems is one of the basic problems in quantum entanglement theory. Mutual unbiased measurement and generalized symmetric information complete measurement are three related concepts in quantum information theory. We use these three kinds of measurements to study the detection of quantum entanglement and obtain a two-body quantum system with different dimensions. On the basis of operator 螖, we obtain a new separability criterion for multibody high-dimensional quantum systems and multi-body multi-level quantum systems. It is proved that they are more effective than the previous criteria. The entanglement criterion on multibody multilevel quantum systems is not limited to the same dimension of subsystems. Therefore, the concept of "separable" can be directly used to detect-non-separable quantum states. In the case of large differences in the dimensions of subsystems, the criterion is improved according to the relationship between dimensions, and the neglected measurement is greatly reduced. The efficiency of the criteria is improved. These separability criteria are more effective than those known before, and can be used to detect the entanglement of unknown quantum states through experiments. This paper is divided into five chapters. We review some basic concepts of entanglement, the concepts of mutual unbiased basis, mutual unbiased measurement and generalized symmetric information complete measurement, and the latest progress in quantum entanglement detection based on them. Based on three kinds of measurements, we study entanglement detection on composite quantum systems with different dimensions of two subsystems, and obtain more effective and widely used separability criteria. We further extend the separability criterion on two-body systems to multi-body high-dimensional systems. So our criterion can be directly used to detect the fixed partitioned-indivisible quantum states, so that we can detect not only whether a given quantum state is entangled, but also the degree of entanglement to a certain extent. We discuss the relationship between entangled witness and separability criterion, and give the entangled witness constructed by the obtained separability criterion. In Chapter 5, we summarize and prospect.
【学位授予单位】：河北师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O413.1

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