產生良好的偏振糾纏光子對在量子資訊科學中是一門相當重要的課題，不論是量子通訊或是量子密碼學，我們都必須使用完美的偏振糾纏光子作為媒介加密並傳送訊息，確保量子通道傳輸過程中的安全性。
本論文使用538.5nm雷射入射一顆週期性極化KTP晶體以第二型自發性降頻轉換(SPDC)，利用一顆晶體一組週期性偏極化，產生偏振糾纏光子，每秒大約產生120對的偏振糾纏光子，再透過貝爾不等式量測S=2.784，足以證明我們的糾纏光子具有良好的糾纏性。接著，使用相同的晶體執行量子密鑰分發-BBM92協定實驗，最後得到原始金鑰大約70 bits/s，QBER大約為10%，安全金鑰比率大約為8.43 bits/s。

Generating polarization-entangled photon pairs is an important subject in quantum information. In quantum communication or quantum cryptography, polarization-entangled photons are required to generate secure keys and increase the security in our quantum channel.
Our PPKTP crystal for generating polarization-entangled photons is composed of one crystal with one periodic poling. The polarization-entangled photons (Bell inequality S=2.784) rate is 120 pair/s. Furthermore, we successfully use our polarization-entangled photon pairs to demonstrate BBM92-QKD experiment with raw key rate 70 bits/s , secret key rate 8.43 bits/s, and QBER=10%.

摘要---i
致謝---iii
目錄---iv
圖表目錄---vi
第一章 實驗目的與動機 ---1
第二章 實驗原理---3
2.1 糾纏態的基本概念與應用---3
2.1.1 量子態(Quantum State)與密度矩陣(Density Matrix)---3
2.1.2 量子糾纏(Quantum Entanglement)---4
2.1.3 貝爾不等式(Bell Inequality)與貝爾態(Bell State) [10] [11]---5
2.2 光子的時間糾纏---9
2.2.1 時間-能量糾纏(Time-Energy Entanglement) [14] [15]---9
2.2.2 時間的可區分性與不可區分性---分光鏡---11
2.2.3 頻率分光的時間可區分性與不可區分性---14
2.3 偏振糾纏光子的製備方法---15
2.3.1 以分光鏡產生糾纏光子---16
2.3.2 非簡併式(Non-degeneracy)偏振糾纏光子對---17
2.4 量子態斷層掃描(Quantum State Tomography) [24]---18
2.4.1 單量子位元(Single Qubit)的量子掃描---18
2.4.2 雙量子位元(Two Qubit)的量子掃描---20
2.5 量子密碼學(Quantum Cryptography)---24
2.5.1 古典密碼學(Classical Cryptography)與量子密碼學---24
2.5.2 不可複製原理(No-Cloning Theorem) [29]---26
2.5.3 BBM92協定(BBM92 Protocol) [6]---27
第三章 實驗架設與數據分析---30
3.1 雷射光源---30
3.1.1 1077 nm外腔雷射光源區---31
3.1.2 綠光的產生---32
3.2 實驗架設區---33
3.2.1 非簡併型偏振糾纏光子(Non-degenerate polarization-entangled photon)的產生---33
3.2.2 非簡併型糾纏光子(Non-degenerate entangled photon)的量測---37
3.2.3 量子密鑰分發-BBM92協定實驗---39
3.3 安全密鑰的產生---42
3.3.1 量子態的隨機選擇與光子的接收---43
3.3.2 訊號的分析方法---44
第四章 討論與總結---48
參考資料---49
附錄---52
附錄一、自發性降頻轉換(Spontaneous parametric down-conversion, SPDC)---52
A.1.1 非線性效應(Nonlinear Effect)---52
A.1.2 相位匹配(Phase Matching)---53
A.1.3 準相位匹配(Quasi-Phase Matching)---54
A.1.4 自發性降頻轉換(SPDC)---56
A.1.5 SPDC光子產生效率推導 [33]---57
附錄二、 BB84協定(BB84 Protocol) [2]---60
附錄三、 E91協定(E91 Protocol) [4]---63
附錄四、資訊理論介紹 [39]---66
附錄五、 BBM92協定的安全性 [30] [40] [41]---68
附錄六、Mυ矩陣的形式---74

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