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研究生: 郭宗承
Kuo, Chung-Cheng
論文名稱: 量子過程能力之研究及其應用
Quantum Process Capability 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: 2018
畢業學年度: 106
語文別: 英文
論文頁數: 49
中文關鍵詞: 量子過程能力量子過程同調性
外文關鍵詞: quantum process capability, quantum process, coherence
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  • 根據量子過程的特性,我們能使狀態展現出在古典力學所不曾出現的性質。而在量子科技中,像是量子計算和量子傳輸等,也面臨處理量子過程的問題,然而在真實的情況下,因為環境產生的干擾以及實驗上的限制,導致過程不符合所預期,甚至過程中的量子特性因此消失,因此如何評估過程中能展現出量子特性的能力就成為一個重要的課題。
    在本篇論文裡,我們發展出一套理論架構歸納和量化量子過程中能導致系統產生非古典效應的能力;接著提出了量子過程能力的概念來幫助我們在量子力學的規範下評估一個過程。而我們也介紹一些工具來評估量子過程能力;這些工具適用於所有能被量子操作理論(quantum operations formalism)所描述的物理過程,而且能在實驗中被實現。最後,在這樣的架構下討論過程創造同調性的能力,並透過所提出的工具來評估不同過程下所能展現的能力。我們的理論有助於了解量子資訊處理(quantum information processing)以及辨別過程是否具有量子特性。

    Physical processes in the quantum regime have unique features that make physical states unusual. Quantum processes themselves are also an essential part of the power of quantum technology. However, practical processes encounter the unexpected environmental disturbance and inevitable experimental conditions, so the quantum characteristics of processes may disappear. So, it is important to evaluate the ability of quantum processes to cause quantum-mechanical effects on physical systems.
    Here, we develop a framework for characterizing and quantifying the ability of quantum processes to cause
    non-classical effects on physical systems. We introduce the concept of quantum process capability that evaluates an experimental process upon the quantum-mechanical specifications. The methods for measuring such capability are introduced. They are experimentally feasible and applicable to all the physical processes described by the general theory of quantum operations. We demonstrate the utility of this framework using several practical examples, such as the ability to create of quantum coherence. The formalism could promote novel recognition of quantum-information processing and classification of dynamical processes in quantum mechanics.

    摘要 i Abstract ii 誌謝 iii Acknowledgements iv Table of Contents v List of Tables viii List of Figures ix Nomenclature x Chapter 1. Introduction 1 1.1. Background 1 1.2. Motivation 2 1.3. Purpose 3 1.4. Outline 4 Chapter 2. Fundamentals of quantum mechanics for thesis 6 2.1. The postulates of quantum mechanics 6 2.1.1. State space 6 2.1.2. Quantum evolution 7 2.1.3. Quantum measurement 8 2.1.4. Composite systems 10 2.2. The density operator 11 2.3. Quantum tomography 12 2.3.1. Quantum state tomography 12 2.3.2. Quantum process tomography 13 Chapter 3. Quantum Process Capability 16 3.1. Basic framework 16 3.1.1. Capable and incapable processes 17 3.1.2. Quantum process capability 18 3.2. Capability measure 19 3.2.1. Properties of capability measure 19 3.2.2. Capability composition 20 3.2.3. Capability robustness 25 3.3. Capability criterion 28 Chapter 4. Applications of Quantum Process Capability 30 4.1. Quantum coherence creation 30 4.1.1. Unitary transformations 32 4.1.2. Projective measurements 34 4.1.3. Noise channels 34 4.1.4. Quantum computation 36 4.1.5. Vacuum Rabi oscillation in a lossy cavity 37 4.1.6. Quantum transport in the Fenna – Matthews – Olson complex system. 39 4.2. Discussion 42 Chapter 5. Summary and Outlook 44 5.1. Summary 44 5.2. Outlook 45 References 47

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