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研究生： 黃妮妮
Huang, Ni-Ni
論文名稱： 量子狀態和過程之量子關聯性的量化及其應用：從量子非局域性到量子通訊
Quantifying Quantum Correlations of Quantum States and Processes and their Applications to Quantum Information Processing: from Quantum Nonlocality to Quantum Communication
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： 139
中文關鍵詞： 量子資訊處理 、量子關聯性 、貝爾非局域性 、古典過程 、量化量子過程
外文關鍵詞： Quantum information processing, Quantum correlations, Quantum nonlocality, Classical process, Quantifying quantum processes
相關次數： 點閱：107  下載：2 
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    • 量子資訊處理利用量子效應，提供了超越古典資訊理論方式之嶄新資訊處理之方法；例如製造、分發、保存糾纏(Entanglement)，以及進行各式操作以完成量子計算或量子通訊任務。為了確認資訊處理結果是由量子方法所得，而非透過古典所模擬，研究糾纏狀態的特性及其經歷任務之過程的量化成為量子資訊處理不可缺乏之步驟。而這樣的探討通常用不同信任性的情境：兩邊皆不可信任、僅有一邊可信任及皆可信任。本論文中就前兩種情境探討了古典狀態與古典過程之量化判別與其應用。我們首先提出了對模組化量子電腦上之網絡型量子隱形傳輸進行判別分析的工具箱：N個位元的鏈狀或箱狀的圖態之網絡型量子隱形傳輸；量化之輸入可信任、輸出不可信任之古典過程模型。此部可延伸至：使用任意多體圖態進行網絡型量子隱形傳輸的一般通用形式；從過程的角度提出純的多體可操控性(genuine multipartite EPR steering) 為非古典網絡型量子隱形傳輸的資源之必要條件。本論文的第二個部分，有別於一般從狀態角度量化貝爾非局域性，我們結合了貝爾非局域性、量子資訊處理常用之狀態及過程斷層掃描及數值方法，開發出同時量化量子狀態及其經歷之過程之工具。我們利用這些工具量化了：晶片尺度之IBM量子電腦邏輯閘運算；光學尺度之雙光子製造及調變；遠距之量子通訊之糾纏分發及量子遙傳上糾纏態製造及所經歷通道的不完美性；三個廣為人知的噪音通道，其顯現出對於噪音強度之不同的靈敏性。本篇論文提供了在兩種不同信任情境下之量化之理論及其應用，其有助於未來量子資訊處理應用上之參考。

    Quantum information processing (QIP) provides a new means for information processing with quantum effects, which outperforms the classical analogue. For instance, using entanglement from generation, distribution, preservation, and manipulations to perform QIP tasks such as quantum computation or quantum communication. Accordingly, quantifying practical entanglement generation and its implemented processes by ruling out any classical strategy of mimicry is indispensable. In general, different combinations of trusted participants in QIP tasks are considered. In this thesis, we investigate two scenarios: only one party is trusted; both parties are not, and their quantitative quantification of quantum correlations of quantum states and processes. First, we propose an identification toolbox, consisting of systematically scalable networking teleportation protocols based on N-qubit cluster state and quantifying tools for examining nonclassical teleportation process on modular quantum computer. Furthermore, we then reveal that genuine multipartite EPR steering is necessary for two essential kinds of quantum networking tasks to faithfully outperform any classical dynamical processes of mimicry. Second, we propose an experimentally feasible method combining Bell nonlocality and tomographic tools for quantifying nonlocality for both states and channels. Our method quantifies different scale QIP tasks. Overall, the toolbox and method proposed in this study provides potential applications to faithfully perform QIP tasks.

    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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3. Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4. Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Chapter 2. Essential Knowledge and Tools 10 2.1. Postulates of quantum mechanics . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.1. Postulate 1 – State space . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.2. Postulate 2 – Evolution . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1.3. Postulate 3 – Quantum measurement . . . . . . . . . . . . . . . . . 14 2.1.4. Postulate 4 – Composite system . . . . . . . . . . . . . . . . . . . 16 2.2. Different types of entangled states . . . . . . . . . . . . . . . . . . . . . . 18 2.3. The density operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4. Entanglement, EPR steering, and Bell nonlocality . . . . . . . . . . . . . . 23 2.5. Quantum teleportation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.6. Quantum tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.6.1. Quantum state tomography . . . . . . . . . . . . . . . . . . . . . . 28 2.6.2. Quantum process tomography . . . . . . . . . . . . . . . . . . . . 29 Chapter 3. Identification of Networking Quantum Teleportation on 14-qubit IBM Universal Quantum Computer 33 3.1. Basic idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.1.1. Modular architecture of the quantum network. . . . . . . . . . . . . 35 3.2. Networking teleportation protocols . . . . . . . . . . . . . . . . . . . . . . 37 3.2.1. Alice’s measurement . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2.2. Participants’s measurements . . . . . . . . . . . . . . . . . . . . . 39 3.2.3. Bob’s operations . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.2.4. Comparison between the original teleportation protocol and our protocols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.3. Identifying quantummechanical process of networking teleportation . . . . 46 3.4. Networking teleportation implemented on ibmq_16_melbourne device . . . 48 3.5. Identification of quantummechanical process of networking teleportation . 55 3.5.1. Detection of genuine multipartite entangled state . . . . . . . . . . 56 3.5.2. Examination of experimental controlled gate . . . . . . . . . . . . . 58 3.5.3. Relation between our process benchmark and calibration parameters of 14qubit IBM quantum processor . . . . . . . . . . . . . . . . . 60 3.6. Genuine multipartite EinsteinPodolskyRosen Steering as resources for networking quantum information processing . . . . . . . . . . . . . . . . . . 64 3.6.1. Opendestination teleportation via any graph state networks . . . . . 65 3.6.2. Genuine multipartite Einstein-Podolsky-Rosen Steering as resources for networking quantum teleportation . . . . . . . . . . . . . . . . 70 3.6.3. Genuine multipartite Einstein-Podolsky-Rosen Steering as resources for quantum secret sharing . . . . . . . . . . . . . . . . . . . . . . 71 Chapter 4. Quantifying Bell nonolocality of States and Channels 77 4.1. The three cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.2. Genuinely classical model states and processes. . . . . . . . . . . . . . . 79 4.2.1. Genuinely classical model states. . . . . . . . . . . . . . . . . . 80 4.2.2. Genuinely classical model processes. . . . . . . . . . . . . . . . 81 4.3. The two tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.3.1. The first test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.3.2. The second test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.3.3. Comparison between the two tests . . . . . . . . . . . . . . . . . . 87 4.3.4. Comparison between the two tests and other related studies . . . . . 87 4.4. The correspondence between the genuinely classical states and the processes 89 4.5. Quantifiers for nonclassical states and their nonclassical processes. . . . . . 90 4.5.1. Nonclassical composition . . . . . . . . . . . . . . . . . . . . . . . 91 4.5.2. Nonclassical robustness . . . . . . . . . . . . . . . . . . . . . . . . 92 4.5.3. Fidelity criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.6. Quantification of experimental imperfection to states and processes . . . . . 94 4.6.1. Quantum computation . . . . . . . . . . . . . . . . . . . . . . . . 95 4.6.2. Biphoton generation and modulation . . . . . . . . . . . . . . . . . 98 4.6.3. Quantum communication . . . . . . . . . . . . . . . . . . . . . . . 101 4.6.4. Quantification of nontrace preserving process projective measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Chapter 5. Summary and Outlook 106 5.1. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.2. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 References 112 Appendix A. The paper submitted for publication 124

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