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研究生： 李秉沅
Lee, Bing-Yuan
論文名稱： 使用不受信任的實驗裝置實現光子量子斷層掃描
Experimental Photonic Quantum Tomography Using Untrusted Devices
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： 2022
畢業學年度： 110
語文別： 英文
論文頁數： 98
中文關鍵詞： 量子態斷層掃描 、閘集斷層掃描 、古典過程 、量化量子過程 、薩格納克干涉儀
外文關鍵詞： Quantum state tomography, Gate set tomography, Classical process, Quantifying quantum processes, Sagnac interferometer
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    • 在量子資訊處理和量子計算任務中，許多應用需要準確且可靠地描述量子狀態以及量子過程的方法，量子斷層掃描是評估量子效應重要的工具；透過斷層解析式精準描述量子資訊系統，具體識別量子狀態及量子過程有無錯誤；而在真實情況下，如量子斷層掃描任務受到環境干擾，或不可避免的實驗缺陷，使得實驗裝置不受信賴，最壞的情況甚至喪失其量子特性，導致實驗結果能被古典物理學所描述。為診斷量子斷層掃描之結果，是由量子方法所得而非透過古典方法所模擬，如何使用不受信任的實驗裝置，實現量子斷層掃描成為一個重要的研究課題。在本論文中，針對以上議題，提出了理論依據以及實驗驗證，在理論上我們將古典模型的概念引入兩種目前廣泛使用之量子斷層掃描工具，分別為量子態斷層掃描 (quantum state tomography) 與閘集斷層掃描 (gate set tomography)，並進一步結合過程斷層掃描與矩陣範數，開發出識別與量化量子過程之工具，為實現使用不受信任的實驗裝置下、執行量子斷層掃描，提供判斷基準。我們利用這些工具，可判別量子態斷層掃描是否喪失其量子特性，也能辦別閘集斷層掃描是否排除被古典物理學所描述的可能。在實驗驗證中，我們使用基於薩格納克干涉儀II型偏振糾纏自發參量下轉換源，產生高保真度糾纏光子對，實現不受信任的實驗裝置下，執行光子狀態斷層掃描，利用提出之基準，判斷最終是否忠實地執行光子狀態斷層掃描。本研究提出之理論方法與實驗驗證，提供未來應用在量子資訊處理與量子計算所需之狀態及過程解析相關任務，如不受信任的量子計算或量子通訊等，用以測試該任務有無忠實地執行。

    In quantum information processing and quantum computation tasks, many applications require accurate and reliable methods for describing quantum states and quantum processes, and quantum tomography is an important tool for evaluating quantum effects; the precise description of quantum information systems through tomographic resolution specifically description quantum states and quantum processes whether there are errors or not; and in real situations, such as quantum tomography procedures is disturbed by the environment or inevitable experimental defects that make the experimental devices untrusted or, in the worst case, lose its quantum properties to the extent that the experimental results can be described by classical physics. In order to diagnose the results of quantum tomography, which are obtained by quantum methods rather than simulated by classical methods, how to realize experimental quantum tomography using untrusted devices has become an important research topic. In this paper, we propose a theoretical basis and experimental validation for the above issues. Theoretically, we introduce the concept of classical model into two widely used quantum tomography tools, namely quantum state tomography and gate set tomography, and further combine process tomography and matrix norm to develop tools for identifying and quantifying quantum processes, providing benchmarks for performing experimental quantum tomography using untrusted devices. We use these tools to identify whether quantum state tomography loses its quantum properties and whether gate set tomography is ruled out of being described by classical physics. In the experimental verification, we use the Sagnac-based type-II polarization-entanglement SPDC-source to generate high fidelity entangled photon pairs to implement experimental photonic state tomography using untrusted devices, and use the proposed benchmarks to determine whether the final photonic state tomography is faithfully performed. The proposed theoretical methods and experimental validation can be used for future applications in quantum information processing and quantum computation, such as untrusted quantum computation or quantum communication, to test whether the task is faithfully performed.

    摘要 i Abstract ii 誌謝 iv Table of Contents v List of Figures ix Nomenclature xi Chapter 1. Introduction 1 1.1. Background 1 1.2. Motivation 2 1.3. Purpose 3 1.4. Outline 4 Chapter 2. Essential Knowledge and Tools 6 2.1. The density matrix and quantum tomography 6 2.1.1. The density operator 7 2.1.2. Quantum state tomography 10 2.1.3. Quantum process tomography 11 2.2. Liouville representation and Pauli transfer matrix 14 2.2.1. Liouville representation 14 2.2.2. Pauli transfer matrix 16 2.3. Bell nonlocality 19 Chapter 3. Theory of Realizing Quantum State Tomography Using Untrusted Measurement Devices 22 3.1. Genuinely classical model 23 3.2. Genuinely classical model in quantum state tomography 25 3.2.1. Basic ideal of combining genuinely classical model with quantum state tomography 26 3.2.2. Application of genuinely classical model in quantum state tomography 27 3.3. Quantifiers for nonclassical process of quantum state tomography 34 3.3.1. Nonclassical composition 34 3.3.2. Nonclassical robustness 35 3.3.3. Fidelity criterion 36 3.4. Comparison of our framework with other tools 39 Chapter 4. Ruling out Classical Simulation of Gate Set Tomography 42 4.1. Gate set tomography 44 4.1.1. Basic idea of gate set tomography 44 4.1.2. Selecting fiducial for gate set tomography 46 4.1.3. Linear inversion gate set tomography algorithm 48 4.2. Genuinely classical model in gate set tomography 51 4.2.1. Basic ideal of combining genuinely classical model with gate set tomography 52 4.2.2. Application of genuinely classical model in gate set tomography 53 4.3. Quantifiers for nonclassical process of gate set tomography 55 4.3.1. Diamond norm 56 4.3.2. Clearest distinction between different target process and genuinely classical model 57 4.4. Example of quantifying imperfection in different processes 58 4.4.1. Prediction of experimental results 59 4.4.2. Approaches for application in optical systems 61 Chapter 5. Quantum State Tomography Using Untrusted Devices in SagnacBased Type-II Polarization-Entanglement SPDC-Source 64 5.1. Sagnac-based polarization-entangled photon source 64 5.1.1. Experiment setup 65 5.1.2. Quality of Sagnac Polarization Sagnac interferometer 68 5.1.3. Temperature controller module 68 5.1.4. Nonlocality tests and state fidelity 73 5.1.5. Application 75 5.2. Demonstration of quantum state tomography using untrusted devices 77 5.2.1. Extended experimental setup 77 5.2.2. Experiment procedure 79 5.2.3. Experiment results 82 5.2.4. Discussion 88 Chapter 6. Summary and Outlook 90 6.1. Summary 90 6.2. Outlook 92 References 94

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