本文關(guān)鍵詞： 量子信息理論 量子關(guān)聯(lián) EPR導(dǎo)引 非定域性 不確定關(guān)系　出處：《中國科學(xué)技術(shù)大學(xué)》2017年博士論文　論文類型：學(xué)位論文

【摘要】：作為量子信息理論的核心,量子糾纏和非定域性不但挑戰(zhàn)了人們對自然的理解和感悟,也日漸成為當(dāng)今量子信息技術(shù)的重要資源。作為對量子糾纏和非定域性的補充,EPR導(dǎo)引可看作這兩個概念間的橋梁。從理論的角度來講,EPR導(dǎo)引既是量子糾纏的充分條件,同時也是非定域性的必要條件。從應(yīng)用的角度來講,EPR導(dǎo)引可以用于在特殊的情境中構(gòu)建一些新穎的通信協(xié)議。本博士論文總結(jié)了作者在讀研期間對EPR導(dǎo)引這一課題的學(xué)習(xí)和研究結(jié)果。在對量子信息基礎(chǔ)知識和EPR導(dǎo)引的歷史做簡要介紹之后,本論文主要討論了EPR導(dǎo)引的判據(jù)及量子導(dǎo)引與非定域性的聯(lián)系。在EPR導(dǎo)引判據(jù)這一部分,本論文主要側(cè)重于線性EPR導(dǎo)引判據(jù)和基于定域不確定關(guān)系的EPR導(dǎo)引判據(jù)。這兩種判據(jù)都十分適于在實際中運用。具體來說,本論文介紹的判據(jù)可以直接運用在任意數(shù)目的測量裝置和任意數(shù)目的測量結(jié)果中,并且減少已有判據(jù)對計算資源的過度需求。同時,本論文也發(fā)展了一套最優(yōu)探測EPR導(dǎo)引的系統(tǒng)方法。作為與其他物理學(xué)概念的聯(lián)系,本論文展示了定域不確定關(guān)系在兩體系統(tǒng)建立的量子關(guān)聯(lián)中發(fā)揮的作用。因此,本論文所展示的EPR導(dǎo)引判據(jù)易于擴展、計算難度低、物理理解清晰,并且與實驗聯(lián)系緊密,為實際應(yīng)用EPR導(dǎo)引——尤其是EPR導(dǎo)引在量子信息任務(wù)中的運用——提供了理論支撐和幫助。在量子導(dǎo)引與非定域性的聯(lián)系這一部分,本論文主要討論了量子導(dǎo)引在Bell不等式的最大違背中發(fā)揮的作用。本文分析了一系列Bell不等式的最大違背,發(fā)現(xiàn)此時Alice的最優(yōu)測量總可以導(dǎo)引Bob的定域量子態(tài)到一定的態(tài)上,從而使相應(yīng)的有效算符的觀測值達到最大。然而,此性質(zhì)在no-signaling等價的意義下并不保持不變。換言之,本論文暗示了這樣一種極為可能的猜測,對于no-signaling意義下等價的Bell表達式,存在一個特殊形式使得該Bell不等式違背最大時,Alice的測量總可以導(dǎo)引Bob的定域量子態(tài)到確定性最大的量子態(tài)上。這一研究結(jié)果豐富了量子信息理論中對非定域性的刻畫,為量子力學(xué)基礎(chǔ)——尤其是量子關(guān)聯(lián)集合的范圍——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.
【學(xué)位授予單位】：中國科學(xué)技術(shù)大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2017
【分類號】：O413

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