EPR导引的判据及量子导引与非定域性的联系

发布时间：2018-02-25 17:49

本文关键词： 量子信息理论量子关联 EPR导引非定域性不确定关系　出处：《中国科学技术大学》2017年博士论文　论文类型：学位论文

【摘要】：作为量子信息理论的核心,量子纠缠和非定域性不但挑战了人们对自然的理解和感悟,也日渐成为当今量子信息技术的重要资源。作为对量子纠缠和非定域性的补充,EPR导引可看作这两个概念间的桥梁。从理论的角度来讲,EPR导引既是量子纠缠的充分条件,同时也是非定域性的必要条件。从应用的角度来讲,EPR导引可以用于在特殊的情境中构建一些新颖的通信协议。本博士论文总结了作者在读研期间对EPR导引这一课题的学习和研究结果。在对量子信息基础知识和EPR导引的历史做简要介绍之后,本论文主要讨论了EPR导引的判据及量子导引与非定域性的联系。在EPR导引判据这一部分,本论文主要侧重于线性EPR导引判据和基于定域不确定关系的EPR导引判据。这两种判据都十分适于在实际中运用。具体来说,本论文介绍的判据可以直接运用在任意数目的测量装置和任意数目的测量结果中,并且减少已有判据对计算资源的过度需求。同时,本论文也发展了一套最优探测EPR导引的系统方法。作为与其他物理学概念的联系,本论文展示了定域不确定关系在两体系统建立的量子关联中发挥的作用。因此,本论文所展示的EPR导引判据易于扩展、计算难度低、物理理解清晰,并且与实验联系紧密,为实际应用EPR导引——尤其是EPR导引在量子信息任务中的运用——提供了理论支撑和帮助。在量子导引与非定域性的联系这一部分,本论文主要讨论了量子导引在Bell不等式的最大违背中发挥的作用。本文分析了一系列Bell不等式的最大违背,发现此时Alice的最优测量总可以导引Bob的定域量子态到一定的态上,从而使相应的有效算符的观测值达到最大。然而,此性质在no-signaling等价的意义下并不保持不变。换言之,本论文暗示了这样一种极为可能的猜测,对于no-signaling意义下等价的Bell表达式,存在一个特殊形式使得该Bell不等式违背最大时,Alice的测量总可以导引Bob的定域量子态到确定性最大的量子态上。这一研究结果丰富了量子信息理论中对非定域性的刻画,为量子力学基础——尤其是量子关联集合的范围——提供了新的思路和方法。
[Abstract]:As the core of quantum information theory, quantum entanglement and nonlocality not only challenge people's understanding and understanding of nature, As a supplement to quantum entanglement and nonlocality, EPR guidance can be regarded as a bridge between these two concepts. From a theoretical point of view, EPR guidance is a sufficient condition for quantum entanglement. EPR guidance can be used to construct some novel communication protocols in special situations. This doctoral thesis summarizes the author's lesson of guiding EPR in his graduate school. After a brief introduction to the basic knowledge of quantum information and the history of EPR guidance, In this paper, we mainly discuss the criterion of EPR guidance and the relation between quantum guidance and nonlocality. This paper mainly focuses on linear EPR guidance criterion and EPR guidance criterion based on local uncertainty relationship. These two criteria are very suitable for practical application. The criteria introduced in this paper can be directly applied to any number of measurement devices and any number of measurement results, and reduce the excessive demand for computing resources. This paper also develops a set of system methods for optimal detection of EPR guidance. As a relation to other physical concepts, this paper shows the role of local uncertainty in quantum correlations established by two-body systems. The EPR guidance criterion presented in this paper is easy to extend, has low computational difficulty, clear physical understanding, and is closely related to the experiment. It provides theoretical support and help for the practical application of EPR guidance, especially the application of EPR guidance in quantum information tasks. This paper mainly discusses the role of quantum guidance in the maximal violation of Bell inequality. In this paper, we analyze a series of maximal violations of Bell inequality and find that the optimal measurement of Alice can always guide the localized quantum state of Bob to a certain state. However, this property is not invariant in the sense of no-signaling equivalence. In other words, this paper implies such a very probable conjecture, that is, for the equivalent Bell expression in the sense of no-signaling, There is a special form in which the Bell inequality can always guide the localized quantum state of Bob to the deterministic maximum quantum state, which enriches the characterization of nonlocality in quantum information theory. New ideas and methods are provided for the foundation of quantum mechanics, especially the range of quantum association sets.
【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O413

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