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研究生： 呂以翔
Lu, Yi-Hsiang
論文名稱： 量子隱形傳態所需之非古典資源的量化及其應用
Quantifying Nonlocal Resources for Quantum Teleportation and Its Applications
指導教授： 李哲明
Li, Che-Ming
學位類別： 碩士
Master
系所名稱： 工學院 - 工程科學系
Department of Engineering Science
論文出版年： 2020
畢業學年度： 108
語文別： 英文
論文頁數： 120
中文關鍵詞： 量子通訊 、量子糾纏 、古典過程
外文關鍵詞： Quantum communication, Quantum entanglement, Classical process
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    • 量子隱形傳態(Quantum teleportation) 使得通訊者兩端藉由分享最大糾纏的愛因斯坦波多爾斯基羅森粒子對及量子量測，完成兩地的未知態傳輸；然而，最大糾纏在製備上或是分發上的瑕疵、或是遭受竊聽後皆會引入古典元素。在此篇論文中，事先分享好的雙古典粒子亦可用於遙傳通訊，我們以此雙古典粒子建立一個純然古典的模型進行量子隱形傳態的模擬，我們好奇於如果通訊兩端利用古典的模擬方式進行量子遙傳通訊，其古典模擬的方式以及其最強的模仿程度，超越此古典過程模型所能描述的過程意味著“真正的量子隱形傳態＂，且其共享量子對的狀態以及量測皆具純然量子特性。我們的工作不僅展示量子隱形傳態在實現上可能遇到的問題，更忠實地揭露雙古典粒子能模擬完成純然量子隱形傳態的最大能力。對於三體複合系統之量子遙傳，我們的結果亦可以提供對於其輸出系統的純的三體非局域性之分析，為實現可信賴的三體量子遙傳任務提供了客觀及嚴謹的指標。

    Quantum teleportation enables an arbitrary unknown state to be transferred from a sender to a receiver, which utilizes both the maximally entangled EisteinPodolskyRosen(EPR) pair and quantum measurements. However, the imperfection of manufacturing or distribution in EPR pair would introduce classical element accordingly. Here, we consider a general scenario where classical pair are shared between a sender (Alice) and a remote receiver(Bob), and by which Alice can transmit an unknown state to Bob with the maximum
    success probability. In this case, we investigate how teleportation can be performed with physical properties. Invaliding such classical teleportation protocol implies genuine quantum teleportation wherein both the shared pair state and the measurement are truly quantummechanical. Our work not only shows how faithful teleportation can be realized, but also the best classical teleportation ability that can simulate quantum teleportation with classical pair. For quantum teleportation of tripartite state, our methods can also identify genuinely tripartite nonlocality of output system. Thus we provide a compelling benchmark for implementing genuine tripartite quantum teleportation.

    摘要i Abstract ii 誌謝iii Table of Contents iv List of Tables viii List of Figures ix Nomenclature xi Chapter 1. Introduction 1 1.1. Background . . . . . . . .. . . . . . . . . . . . . . 1 1.2. Motivation . . . . . . . . . . . . . . . . . . . . . 3 1.3. Purpose . . . . . . . .. . . . . . . . . . . . . . 4 1.4. Outline . . . . . . . . . . . . . . . . . . . . . . . 5 Chapter 2. Essential Knowledge and Tools 7 2.1. Postulates of quantum mechanics . . . . . . . 7 2.1.1. Postulate 1 – State space . . . . . . . 8 2.1.2. Postulate 2 – Evolution . . . . . . . . . 9 2.1.3. Postulate 3 – Quantum measurement . . . . . . 10 2.1.4. Postulate 4 – Composite system . . . . . . . 12 2.2. Density operator . . .. . . . . . . . . . . . 14 2.3. Quantum tomography . . . . . . . . . . . . . . . 17 2.3.1. Quantum state tomography . . . . . . .. . . . . 18 2.3.2. Quantum process tomography . . . . . . . . . . 19 Chapter 3. Quantifying Quantum Teleportation with Nonlocal Resources 22 3.1. Introduction to quantum teleportation . . . . . . . 23 3.2. Basic concept of three classical mimicries . . . . . 24 3.2.1. Characterizing teleportation process . . . . .. . 26 3.2.2. Classical teleportation model . . . .. . . . . 28 3.2.3. Genuinelyclassical teleportation model . . . . . 29 3.2.4. Classical teleportation model as a special case of genuinelyclassical teleportation model . . . . . . . . 31 3.2.5. Distinction between genuinelyclassical teleportation model and genuinelyclassical process . . . . . . . . . 34 3.3. Quantifying quantum teleportation . . .. . . . . . 35 3.3.1. Methods for quantifying teleportation . . . . . 35 3.3.2. Fidelity criterion . . . . . . . . . . . . 36 3.3.3. Quantum composition . . . . .. . . . . . . 38 3.3.4. Process robustness . . . . . . . . . . . . 39 3.4. Examples of teleportation using noisy resource .. . 40 3.4.1. Identification of teleportation using Werner state as resource . . . . 41 3.4.2. Effects of noise on one of the shared pair used in teleportation as resource . . . . . . . . . 45 3.5. Discussion and Applications . . . . . . 48 3.5.1. Simulating any dynamical process with genuinelyclassical teleportation 48 3.5.2. Identifying quantum information processingremote state preparation 49 Chapter 4. Quantum Teleportation of GenuinelyTripartite Nonlocal State 51 4.1. Resource required for tripartite quantum teleportation. . . . .. 51 4.1.1. Preparation of chaintype tripartite cluster state 52 4.1.2. Preparation of closedtype tripartite cluster state 53 4.2. Identifying genuinelymultipartite nonlocal state and genuinelyclassical multipartite state . . . . . . . . . 55 4.2.1. Definition of genuinelytripartite nonlocal state .59 4.2.2. Methods for identifying genuinelytripartite nonlocal state . . . . . 59 4.2.3. Chaintype genuinelyclassical tripartite teleportation model: first model 73 4.2.4. Chaintype genuinelyclassical tripartite teleportation model: second model . . .. . . . . .. . 82 4.2.5. Closedtype genuinelyclassical tripartite eleportation model . . . . 90 4.2.6. Identifying genuinelymultipartite nonlocal state 98 4.3. Summary and discussion . . .. . . . . . . . . . . . 99 Chapter 5. Summary and Outlook 100 5.1. Summary . . . . . . . 100 5.2. Outlook . . . . . . . 101 References 103 Appendix A. Semidefinite programming 108 Appendix B. Maximum state fidelity and bilocal correlation of ρψ3c1,out{1, 23} via programming 111 Appendix C. Maximum state fidelity and bilocal correlation of ρψ3c1,out{2, 13} via programming 116

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