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研究生： 孫聖諺
Sun, Sheng-Yan
論文名稱： 實驗上識別產生六體糾纏之光子干涉能力
Experimental Capability of Photon Interference for Generating Six-Photon Entanglement
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： 2023
畢業學年度： 111
語文別： 英文
論文頁數： 117
中文關鍵詞： 量化量子過程 、糾纏生成與保存 、六光子糾纏 、光纖傳輸糾纏光子 、糾纏目擊
外文關鍵詞： Quantification quantum processes, Entanglement generation and preservation, Six-photon entanglement, Fiber transfer entangled photon, Entanglement witness
相關次數： 點閱：44  下載：2 
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    • 在量子光學系統上，產生多光子糾纏實驗中最重要的操作為光子干涉，沒有他無法實現多光子糾纏，他是一種產生量子糾纏的操作。量子糾纏為量子力學中獨有的性質，在進行量子糾纏相關操作時，量子糾纏在操作中的產生或保存與否決定整個量子任務的成敗。但如今對於干涉操作中如何量化產生或保存糾纏仍未明朗。在本研究中我們應用了能夠量化光子干涉過程中產生與保存糾纏的能力理論，並首次實際使用於兩對光子的干涉實驗中，以產生糾纏之能力來預測干涉操作產生之四體格林伯格-霍恩-蔡林格態(GHZ 態)。我們更進一步引入噪音至干涉操作中，並應用過程保真度下界估計與我們分析過程能力的方式，進一步表明不完美干涉操作是如何影響干涉操作產生或保存糾纏的能力，並驗證我們工具在實際應用的有效性。更進一步，在光量子系統中，多光子糾纏的數目代表著我們執行量子任務的能力。基於這一觀點，我們成功建立了基於光纖傳輸的六光子糾纏工程，奠定製造高度複雜光子網絡的能力。包含了在糾纏光子傳輸過程中偏振演化的補償方法，同時應用了一種能夠快速搜尋干涉重合的技術，以高效地建立多光子糾纏態。最後，我們透過光子量子過程能力的分析技術，在不執行量子斷層掃描下評估了我們所建立的糾纏態與六體GHZ 態之間的接近程度，並實際透過兩個設置之糾纏目擊來驗證所製造的狀態具有真正的多體糾纏。結果顯示，我們的六重符合糾纏光子產率約為每三小時250 顆，六體狀態的保真度經由過程能力方法估計為0.5203，糾纏目擊數值為-0.0801±0.0037，其具有真正的多體糾纏，也表明了我們工具的實用性。

    In quantum optics systems, photon interference is the crucial operation for generating multiphoton entanglement in experiments. Without it, achieving multiphoton entanglement would not be possible. Quantum entanglement is a unique property of quantum mechanics and is a vital resource in quantum information processing. During operations related to quantum entanglement, whether entanglement is generated or preserved within the operation determines the success of the entire quantum task. However, quantifying entanglement generation or preservation in interference operations remains unclear. In this study, we applied the theoretical framework of quantifying the capability of generating and preserving entanglement in photon interference processes. For the first time, we implemented this framework in an experimental setup involving the interference of two pairs of photons. We utilized the entanglement generation capability to predict the creation of the four-photon Greenberger-Horne- Zeilinger (GHZ) state through interference operations. Furthermore, we introduced noise into the interference operation and employed the process fidelity lower bounds, along with our analysis of process capabilities. This approach further illustrates how imperfect interferenceoperations impact the ability to generate or preserve entanglement. It also validates the effectiveness of our methodology in practical applications. Furthermore, the number of multiphoton entanglements in the photonic quantum systems represents our capacity to perform quantum tasks. With this perspective, we successfully established a six-photon entanglement based on optical fiber transmission, laying the foundation for creating highly complex photonic networks. This encompassed compensation methods for polarization evolution during entangled photon transmission alongside a technique for efficiently locating interference overlap, facilitating the efficient creation of multiphoton entangled states. Finally, utilizingthe analysis technique of photon quantum process capabilities, we evaluated the proximity between the entangled states we established and the six-photon GHZ state without the need for quantum tomography. We validated the genuinely multipartite entanglement of the created states through two local measurement settings. The results revealed that our six-fold entangled photon generation rate is approximately 250 every three hours. The fidelity of the six-photon state, estimated using the process capability approach, is 0.5203. The entanglement witness value is -0.0801 ± 0.0037, indicating genuine multipartite entanglement and highlighting the practicality of our methodology.

    摘要 i Abstract ii 誌謝 iv Table of Contents v List of Tables ix List of Figures x Nomenclature xii Chapter 1. Introduction 1 1.1. Background 1 1.2. Motivation 3 1.3. Purpose 4 1.4. Outline 6 Chapter 2. Foundational Knowledge and Tools for the Proposed Framework in This Research 8 2.1. The density operator 9 2.2. Bell states, Greenberger-Horne-Zeilinger states, and graph states 11 2.3. Quantum tomography 14 2.3.1. Quantum state tomography 15 2.3.2. Quantum process tomography 16 2.4. Quantum process capability 21 2.4.1. Capability composition α 22 2.4.2 Capability robustness β 23 2.4.3 Quantum criterion 24 Chapter 3. Quantification of Experimental Photon Interference Capability 25 3.1. Capability of entanglement generation and preservation 26 3.1.1. Construction of incapability process χI,pre, χI,cre 27 3.1.2. Entanglement preservation capability composition αpre and robustness βpre 28 3.1.3. Entanglement generation capability of composition αcre and robustness βcre 30 3.2. Quantification photon interference operations for generate four-photon GHZ state 33 3.2.1. The entangled sources: Type-II spontaneous parametric down-conversion (SPDC) 33 3.2.2. The quantum interference and interference operation 35 3.2.3. Experimental setup 39 3.2.4. Results of the photon interference capability 45 3.3. Estimating the four-photon state fidelity with entanglement generation capability 48 3.3.1. Experimental measurement of four-photon state fidelity with QST and entanglement witness observable M 49 3.3.2. Analysis and estimation of |G4⟩ fidelity with the QPC method 50 3.4. Consideration of imperfect photon fusion and analyze the trend of process capability degradation without doing QPT 54 3.4.1. Experimentally measuring the process fidelity lower bound 54 3.4.2. Calculating the capability of entanglement generation and preservation using process fidelity lower bounds 57 Chapter 4. Generation and Verification of Six-Photon Entanglement 62 4.1. The second interferometer for four-photon entanglement 64 4.1.1. Generation and fiber-based transmission of the third photon pair 64 4.1.2. Optical fiber polarization compensation 66 4.1.3. Time-tag analysis of pulse laser signals in an interferometer 68 4.1.4. Results of the second set of four-photon entanglement 71 4.2. Six-photon entanglement establishment 73 4.2.1. Experimental setup for six-photon entanglement 74 4.2.2. Estimating the fidelity of the six-photon GHZ state using entanglement generation capability without performing quantum tomography 77 4.2.3. Verification of genuine six-photon entanglement 82 Chapter 5. Summary and Outlook 85 5.1. Summary 85 5.2. Outlook 87 References 90 Appendix A. The details of the process capability lower bound 96 Appendix B. Experimental raw data 103 B.1. The basis fidelity of each δτ of 1st and 2nd fusion operation 103 B.2. RSP method, the expectation value of output state 104 B.3. Local wave plate rotation method, the expectation value of output state for QPT 106 B.4. The expectation value of measurement settings with {I, X, Y, Z} ⊗4 via QST 108 B.5. The expectation values of the individual measurement settings of the 2nd |G4⟩ state 110 Appendix C. Additional analysis method for estimate |G6⟩ state fidelity 111 C.1. Analyzing six-photon entanglement state fidelity using varied experimental information through process capability 111 C.2. Estimate six-photon entanglement state fidelity using another type of input state model 115

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