
系統識別號 
U00261901201610295000 
論文名稱(中文) 
多體之愛因斯坦—波多爾斯基—羅森操控性與量子資訊處理

論文名稱(英文) 
Multipartite EinsteinPodolskyRosen Steering and 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 
1 
出版年 
105 
研究生(中文) 
呂彥德 
研究生(英文) 
YenTe Lu 
學號 
N96034251 
學位類別 
碩士 
語文別 
英文 
論文頁數 
91頁 
口試委員 
指導教授李哲明 口試委員陳岳男 口試委員周忠憲

中文關鍵字 
多體EPR操控性
量子資訊處理
量子祕密分享

英文關鍵字 
Multipartite EPR steering
Quantum information processing
Quantum secret sharing

學科別分類 

中文摘要 
愛因斯坦—波多爾斯基—羅森 (EPR) 操控性是一種介於糾纏與貝爾非局域性的二體量子關聯特性，它可以確保兩個異地通信者建立安全密鑰，即使當有一方的量測裝置是不可信任的。本論文描述了由二體至多體之EPR操控性的基本特徵，並進一步提出從實驗上可實現的方法來偵測此多體之操控性；此方法具有極佳的噪音容忍度，並且適用於廣泛的多體糾纏系統，其可進一步應用在當有不可信任的量測裝置存在於量子資訊處理的方案中，例如量子計算和量子通訊；我們亦結合了上述偵測多體之EPR操控性的方法開發出一種實驗上有效率的方式，用來確認當存在不可信任的量測裝置或是參與者的多體量子祕密分享方案之安全性，其有助於將來操控性質在量子資訊課題上關於安全性的探討。

英文摘要 
EinsteinPodolskyRosen (EPR) steering, which is an intermediate type of quantum correlation sitting between entanglement and Bell nonlocality, allows two parties to establish quantum secret key even if the measurement devices of one party are untrusted. Extending the concept of bipartite EPR steering, here we describe the characteristics of multipartite EPR steering and then propose an experimentally feasible method to detect the multipartite EPR steerability. Our formalism has high noise tolerance, and it can be used to certify the steerability for a large class of multipartite quantum entangled systems. In addition, combining with the above method of detecting the multipartite EPR steerability, we develop an efficient way to ensure the security of multiparty quantum secret sharing in the presence of uncharacterized measurement apparatuses or parties, which provides potential applications to the secure quantum information tasks.

論文目次 
中文摘要 I
Abstract II
Acknowledgements III
List of Figures and Tables VI
Nomenclature VII
Chapter 1 Introduction 1
1.1 Research background 1
1.2 The motivation of study 4
1.3 Research purpose 6
1.4 The outline of dissertation 6
Chapter 2 Fundamentals of quantum mechanics for quantum information science 8
2.1 The postulates of quantum mechanics 8
2.1.1 State space 9
2.1.2 Quantum evolution 15
2.1.3 Quantum measurement 16
2.1.4 Composite systems 22
2.2 The density operator 24
2.2.1 General properties of the density operator 24
2.2.2 The reduced density operator 30
2.3 Quantum entanglement 32
2.3.1 Bell inequality 32
2.3.2 Quantum computation 35
2.3.3 Quantum teleportation and dense coding 41
Chapter3 Certifying genuine multipartite Einstein PodolskyRosen steering 45
3.1 Introduction 47
3.1.1 The oneway quantum computing 48
3.1.2 Graph states and genuine multipartite EPR steering 50
3.2 Quantum steering witnesses 52
3.2.1 Genuine multipartite steering witnesses derived from full state knowledge 53
3.2.2 Robustness of steering witness 56
3.3 Certifying the steerability from the experimental state fidelity 57
3.3.1 Ensuring genuine multipartite EPR steering for cluster states 58
3.3.2 Ensuring genuine multipartite EPR steering for Dicke states 60
3.4 Discussion 62
Chapter 4 Multipartite steering witnesses for secure quantum communication 65
4.1 Introduction 66
4.1.1 Quantum secret sharing 67
4.1.2 Genuine multipartite steering for multiparty quantum communication 70
4.2 Quantum steering witnesses for secure quantum communication 72
4.3 The noise tolerance of the steering witnesses 78
4.4 Discussion 81
Chapter 5 Summary and outlook 83
5.1 Summary 83
5.2 Outlook 84
Reference 85

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