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系統識別號 U0026-1901201610295000
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 Einstein-Podolsky-Rosen 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) Yen-Te 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 Einstein-Podolsky-Rosen (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- Podolsky-Rosen steering 45
3.1 Introduction 47
3.1.1 The one-way 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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