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系統識別號 U0026-2807201616025800
論文名稱(中文) 量子非實在性量度與其在量子資訊上的應用
論文名稱(英文) Quantification of non-realistic features and applications to quantum information processing
校院名稱 成功大學
系所名稱(中) 工程科學系
系所名稱(英) Department of Engineering Science
學年度 104
學期 2
出版年 105
研究生(中文) 陳建廷
研究生(英文) Chien-Ting Chen
學號 N96034439
學位類別 碩士
語文別 英文
論文頁數 98頁
口試委員 指導教授-李哲明
召集委員-周忠憲
口試委員-羅信斌
中文關鍵字 實在性  量子非實在性  量子資訊處理 
英文關鍵字 Realism  Quantum non-realistic features  Quantum information processing 
學科別分類
中文摘要 古典實在性理論無法完全地描述量子狀態,這種量子非實在性已被利用於偵測純然之量子效應,並已被應用於量子資訊處理之中,然而,至今為止還沒有量化量子非實在性的研究方案;本論文先定義一個可被古典實在性理論描述的狀態,並定義一個可使任意狀態轉變成此種狀態的過程,然後以此進一步提出兩種量度來量化量子狀態與過程的量子非實在性,透過這兩種量度,我們整理出任意的量子純態與任意的么正轉換具有最多的量子非實在性,此外,我們研究這兩種量度在量子資訊處理上的應用,例如量測量子通道的量子非實在性以及評估量子邏輯閘的效能,最後,我們亦比較了量子非實在性量度與其他非古典特性的量度,如量子同調性,並指出它們之間的差異性。
英文摘要 Quantum states are not completely described by the classical theory of realism. Such quantum non-realistic features provide tools to detect quantum effects and have applications to quantum information processing. There is, however, no scheme for quantifying non-realistic features. Here we first define a reference state that can be described by the classical realistic theory. A quantum process that changes any states into this reference state is also introduced. We then further propose two measures to quantify the non-realistic features of quantum state and quantum process. With these two novel quantifiers, we show that any pure states and any unitary transformations are the states and the processes of maximal non-realistic features, respectively. Furthermore, we also apply these quantifiers to quantum information processing, such as quantifying non-realistic features of quantum channels and evaluating the performance of quantum gates. Finally, we compare our measures with a quantum coherence quantifier in detail.
論文目次 中文摘要 I
Abstract II
Acknowledgements III
Table of Contents IV
List of Figures VII
List of Tables VIII
Nomenclature IX
Chapter 1 Introduction 1
1.1 Research background 1
1.2 The motivation for this study 3
1.3 Research purpose 5
1.4 The outline of dissertation 6
Chapter 2 Fundamentals of quantum mechanics for quantum information processing 8
2.1 State space 8
2.2 Evolution 11
2.3 Quantum measurement 12
2.4 Composite systems 14
2.5 The density operator 15
2.6 Quantum noise and quantum operation 22
2.6.1 Quantum operations formalism 22
2.6.2 The superoperator and the operator sum representation 23
2.6.3 Examples of quantum noise and quantum operation 25
2.7 Master equation 29
2.7.1 Markovian evolution 29
2.7.2 The Lindbladian and the master equation 30
2.8 Quantum process tomography 33
2.9 Distance measures 36
Chapter 3 Quantum discord and quantum coherence witness 38
3.1 Quantum discord 38
3.1.1 Mutual information in classical information theory 39
3.1.2 The mutual information in quantum information theory 41
3.1.3 Quantum discord 42
3.2 Quantum coherence witness 47
3.3 Detecting quantum coherence of an open double quantum dot system 49
3.3.1 Open double quantum dot system 50
3.3.2 Discussion 51
Chapter 4 Quantifying non-realistic features of quantum states and processes 55
4.1 The assumption of underlying objective reality for quantum mechanics 55
4.1.1 Ontic and epistemic views 56
4.1.2 Ontological models 57
4.2 The assumptions of objective reality 59
4.3 Detecting non-realistic features of quantum states 60
4.4 Quantifying non-realistic features of quantum states 62
4.4.1 The reality state 62
4.4.2 The quantification of the non-realistic features of quantum states 63
4.4.3 The state of the least objective reality 65
4.5 Quantifying non-realistic features of quantum processes 67
4.5.1 The reality process 68
4.5.2 The quantification of the non-realistic features of a quantum process 69
4.5.3 The process of the least objective reality 70
4.5.4 Detecting non-realistic features of a quantum noise channel 71
4.6 Evaluating the performance of a quantum gate with quantification of the non-realistic features of a quantum process 74
4.6.1 Relationship between process fidelity and the process measure of non-realistic features 75
4.6.2 Application of the relationship between the process measure of non-realistic features and process fidelity 77
4.7 Comparing non-realistic features with coherence 86
Chapter 5 Summary and Outlook 90
5.1 Summary 90
5.2 Outlook 91
Reference 94
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