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系統識別號 U0026-0308201522584100
論文名稱(中文) 量子可操控性偵測與量子密碼學
論文名稱(英文) Detection of Quantum Steering and Its Application to Quantum Cryptography
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 103
學期 2
出版年 104
研究生(中文) 邱靖益
研究生(英文) Ching-Yi Chiu
學號 N96011546
學位類別 碩士
語文別 中文
論文頁數 115頁
口試委員 指導教授-李哲明
口試委員-周忠憲
口試委員-羅信斌
中文關鍵字 量子可操控性  量子資訊理論  量子竊聽  量子密碼 
英文關鍵字 Quantum steering  Quantum information  Quantum eavesdropping  Quantum cryptography 
學科別分類
中文摘要 Einstein-Podolsky-Rosen(EPR)可操控性描述了對於一個量子系統進行測量可以製備另一個系統狀態的性質,其起源於Schrödinger對於Einstein等人探討量子力學理論完備性之Einstein-Podolsky-Rosen悖論研究的回覆。本論文提出一個關於單系統可操控性的新穎概念,不同於兩個系統的EPR可操控性,其描述了傳送者量測系統並將其傳遞予接收者時,傳送者所進行的量測能製備接收者收到之系統狀態。我們設計了能夠偵測系統是否具此性質的實驗方案,並描述不具有可操控性的情境用以推導量子目擊;並證明當系統具有此性質時,我們可傳遞此系統完成安全密鑰分配,此外,我們亦說明如何將單系統量子目擊應用於偵測EPR可操控性。
英文摘要 We propose a new concept of steering for single quantum d-dimensional systems and devise novel quantum witnesses to detect steerability which are applicable for both single-system steering and Einstein-Podolsky-Rosen (EPR) steering. These witnesses are useful to quantum communications for securing channels against both cloning-based individual attack and coherent attacks. It may be interesting to investigate further the steering transfer in quantum cloning machine.
Key words: Quantum steering, Quantum information, Quantum eavesdropping, Quantum cryptography.
論文目次 目錄

中文摘要 I
Abstract II
致謝 VIII
圖表目錄 XI
符號說明 XII
第一章 緒論 1
1.1 研究背景 1
1.2 研究動機 4
1.3 研究目的 5
1.4 論文架構 5
第二章 量子力學與四大公設 7
2.1 狀態向量 7
2.2 狀態的演化 8
2.3 量子系統的測量 10
2.4 複合系統 11
2.5 密度算符 13
2.6 開放量子系統 16
2.7 貝爾不等式與局域實在性 19
2.8 EPR 量子可操控性 22
第三章 古典資訊理論與量子資訊理論 27
3.1 古典資訊理論與夏農信息熵 27
3.2 量子資訊理論 30
3.2.1 量子信息熵與馮紐曼熵 31
3.2.2 信息熵的不確定性原理 34
3.2.3量子通訊與Holevo 邊界 35
第四章 量子密鑰分配與量子複製 40
4.1 BB84協議 41
4.2 E91協議 43
4.3 量子不可複製原理 44
4.4 包立量子複製 45
4.5 個別竊聽、集體竊聽與同調性竊聽 49
4.6 多維度量子系統密鑰分配對於個別竊聽之安全性 52
4.7 多維度系統秘鑰分配對於同調性與集體攻擊的安全性 58
第五章 單系統量子可操控性 65
5.1 時態性可操控性方案 65
5.2 單系統量子可操控性方案 71
5.2.1 可操控性的喪失與實在性系統之描述 73
5.2.2 可操控性偵測與量子目擊 78
5.2.2.1 條件機率可操控性量子目擊 79
5.2.2.2 信息熵可操控性量子目擊 81
5.2.3 可操控性量子目擊與量子秘鑰安全性 83
5.2.4 量子目擊的強健度 86
5.2.5 量子目擊與EPR可操控性 88
5.2.6 時態性可操控性不等式證明與不具可操控性系統描述 94
5.2.7 單系統量子目擊與時態性可操控性不等式比較 96
5.3 量子目擊的特性 99
第六章 驗證實驗 101
6.1 多維度貝爾不等式 101
6.2 多維度光子系統貝爾不等式驗證實驗設置與其應用於量子目擊 103
第七章 結論與未來展望 107
7.1 結論 107
7.2 未來展望 108
參考文獻 111
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