量子态可分性判定与纠缠度量

发布时间：2018-06-23 05:48

本文选题：量子纠缠 + 可分性判定准则　；参考：《电子科技大学》2016年博士论文

【摘要】：在科技不断的发展过程中,物理学尤其是量子物理越来越和计算机科学、信息科学等学科紧密的联系在了一起,随之产生了量子信息学。而在量子信息学中,量子纠缠现象是一种独特的资源,在量子信息学的绝大多数应用中起着十分关键的作用。近几十年来,量子纠缠吸引了越来越多的关注,人们为深入理解纠缠现象付出了巨大的精力,并努力使之在实际应用中发挥重要作用。例如,运用纠缠可以将通信安全提升到一个新的高度。而量子计算将计算的概念焕然一新,以此为基础的量子计算机更将会极大的改变计算机科学。毫无疑问,量子纠缠这一令人瞩目的研究将会极大的推动科技和社会的不断进步。论文以量子信息论和量子力学为背景,重点研究了纠缠的判定(或检测)和量化问题。给定一个量子态(状态),如何判断它是否是纠缠态,或是可分态?这就需要用到可分性判定准则(也称为纠缠判据)。当前,已存在很多可分性判定准则。但是直到现在,还没有一个通用的判定方法,每一种方法都有特定的适用场合和局限性。如果已知一些量子态是纠缠的,我们是否可以去量化它们所含有“纠缠”的多少,以来比较哪个状态含有的“纠缠”多。因为含有“纠缠”多的状态在实际应用中可能效用更大或是更可靠,而“纠缠度(量)”这一概念就可以作为含有纠缠多少的定量描述。如今,大量的纠缠度定义被提出,它们分别有着不同的用途和考察角度,但是它们当中大多难以计算。综上,本论文就是旨在提出新的即容易理解、又方便计算的可分性准则和纠缠度。主要创新如下:1.提出了基于量子态密度矩阵的秩的可分性判定准则,该准则可适用于任意多体系统纯态。证明了一个多体量子态的(约化)密度矩阵的秩与纠缠有着密切的关系,它可以用来检测纠缠是否存在。通过考察一个9)-qudit纯态|?的29)-1-1个独立的密度矩阵的秩,就可以判定该状态是部分可分的、全可分的、或是一个真正的9)-qudit纠缠态。该方法对于纠缠的检测是一个充分必要条件。2.提出了基于量子态系数矩阵的秩的可分性判定准则。该准则经证明也是一个检测纠缠的充分必要条件,并且与基于密度矩阵的秩的方法是等价的。两种方法都便于理解和计算,还可以帮助我们找到任意一个多体纯态的具体可分形式。3.基于量子态的系数矩阵,本文提出一个新的纠缠度。把系数矩阵的行列看作向量,该纠缠度定义只需要计算其向量长度及向量之间的角度。通过与著名的纠缠度定义concurrence作对比,验证了本文提出的方法是行之有效的,并且经证明它满足一个任意纠缠度定义都必须满足的一些条件。该纠缠度计算简单,且具有清楚的几何意义。4.基于量子态的(约化)密度矩阵,本文还提出一个新的适用于任意9)-qudit态的多体纠缠度。经证明,它也是一个有效的纠缠度定义,该方法能够分辨出相对高度纠缠和最大纠缠。以上所提出的方法都经过了具体计算实例的对比验证,它表明我们所提出的方法易于理解,计算简单,具有良好的适用性。
[Abstract]:In the course of the continuous development of science and technology, physics, especially quantum physics, has become more and more closely linked with computer science, information science and other disciplines, resulting in quantum informatics. In quantum informatics, quantum entanglement is a unique resource and plays a very important role in the vast majority of applications of quantum information. In recent decades, quantum entanglement has attracted more and more attention. People have made great efforts to understand entanglement in depth and try to play an important role in practical applications. For example, the use of entanglement can raise the security of communication to a new high degree. The quantum computer will greatly change the computer science. There is no doubt that quantum entanglement, a remarkable research, will greatly promote the continuous progress of science and technology and society. The thesis focuses on the determination (or detection) and quantization of entanglement in the context of quantum information and quantum mechanics. State (state), how to judge whether it is an entangled state or a separable state? This requires the use of separability criteria (also known as entanglement criteria). At present, there are many separability criteria. But until now, there is no general determination method, each method has a specific application and limitations. If some of the methods are known, some of them are known. The quantum state is entangled. Whether we can quantify the number of entanglement they contain and which states have more entanglement. Because the state of "entanglement" may be more effective or more reliable in practical applications, the concept of "entanglement" can be used as an entanglement. A large number of definitions of entanglement have been proposed, and they have different uses and angles of investigation, but most of them are difficult to calculate. To sum up, this paper is aimed at proposing a new separability criterion and entanglement degree which is easy to understand and convenient to calculate. The main innovations are as follows: 1. the quantum density matrix based on the quantum state matrix is proposed. The criterion for determining the separability of a rank, which can be applied to the pure state of any multibody system. It is proved that the rank of a (Reductive) density matrix of a multibody state is closely related to the entanglement. It can be used to detect the existence of entanglement. By examining the rank of the -1-1 independent density matrix of a 9) -qudit pure state? It can be judged by the rank of the independent density matrix. The state is partially separable, all separable, or a real 9 -qudit entanglement state. This method is a sufficient and necessary condition for the detection of entanglement..2. proposes the criterion of separability based on the rank of the quantum state coefficient matrix. The criterion is proved to be a sufficient and necessary condition for detecting entanglement and is also a density matrix based on the density matrix. The rank method is equivalent. The two methods are easy to understand and calculate. We can also help us find the coefficient matrix of the specific separable form of a multibody pure state.3. based on the quantum state. In this paper, we propose a new degree of entanglement. The ranks of the coefficients matrix are regarded as a vector. The definition of the degree of entanglement only needs to calculate the length and vector of the vector. By comparing with the famous entanglement definition concurrence, it is proved that the method proposed in this paper is effective and proves that it satisfies some conditions that the definition of any entanglement degree must be satisfied. The entanglement is simple and has a clear geometric meaning.4. based on the quantum state (reduced) density matrix. This paper also proposes a new multibody entanglement degree for any 9 -qudit state. It is proved that it is also an effective definition of entanglement. The method can distinguish relative high entanglement and maximum entanglement. The proposed method has been verified by the comparison of concrete examples. It shows that the method we proposed is easy to understand and calculate. It is simple and has good applicability.
【学位授予单位】：电子科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O413

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