本篇論文在研究探討我們一般在做量子通訊(Quantum communication)時所遭遇到環境擾動的問題，像是分層的空氣流速不同或是不同區域溫度的差異，都會影響空氣的折射率分布，因而形成流體力學中的所謂亂流(Turbulence)，這樣的擾動也會影響到光的狀態。
並且，由於光的偏振方向是最為常見作為編碼的手段，為了研究在偏振這個自由度下的擾動，我們建立了一套模擬偏振擾動的系統，能夠達到像是光纖對偏振的旋轉效果，並給予可以人為控制的擾動，稱作亂流系統。在量子通訊上，作為資訊傳遞通道的性質就相當重要，因此，我的研究想要利用這套系統，探討在偏振這個自由度下，這種擾動對於光子偏振狀態，甚至是雙光子關聯性上的演化，以及以此作為傳輸通道，嘗試分析偏振關聯性在去相干影響下的保存。
在過去的實驗中，我們確實可以看出量子貝爾態(Bell-state)在我們既有的亂流系統中，有並發值(concurrence)下降的現象，表示糾纏程度經過亂流系統後逐漸降低。因此我們想更仔細針對貝爾態在亂流通道影響下做其他關聯性的測量，觀察各個指標影響程度的差異以及他們之間的相對關係。對於這些現象，我們也嘗試從量子通道的角度去分析，更進一步了解整個亂流系統。
經過層層的討論後發現，反對稱的貝爾態不管是哪一種亂流通道，在任何一種關聯性指標上都不會受到影響，並且，我們建立了一個物理圖象模型，透過這個圖象的理論計算，我們能夠預測各種貝爾泰經過亂流通道其糾纏度消失的程度。此外，從實驗的結果也可以發現一些系統在使用上的缺陷，對此我們也提出了理論模型和實驗上的改進。

In this thesis, we aim to solve the problem of environment disturbance that people usually confront when implementing Quantum communication, such as the difference of air fluid velocity between layers or temperature between different regions. These factors will lead to a distribution of refractive index and form the phenomenon in fluid dynamics—Turbulence. The disturbance will also affect the state of light.
Moreover, since the polarization direction of light is the most common encoding method, we established a system to simulate the disturbance of polarization under such degrees of freedom. The system can rotate polarization of light just like when we transmit light in an optical fiber. And it can produce man-made modulation imitating disturbance of fluid. So we also call it Turbulent System. Besides, it is also important to clarify the property of a channel transmitting information in quantum communication. Therefore, I try to use this system to investigate the evolution of the polarization state of photons and even two-photon correlations under the degrees of freedom of polarization. Also use the system as a transmission channel to analyze the survival of polarization correlation under the influence of decoherence.
In the past experiments, we saw decrease of concurrence for Bell-states in our Turbulence System, which means entanglement get weaker when going through our system. Therefore, we want to focus on other measurements of correlations and observe the influence between different indexes. For these phenomena, we also try to analyze them from the perspective of quantum channels, so as to further understand the entire turbulent system.
From the results of experiments, we found that no matter which index we take care of, the anti-symmetric Bell-state will always survive. Moreover, we construct a physical model. Through calculating from this model, we can predict the decreasing of degree of entanglement when each bell state passing through our turbulence device. In addition, we also find some defect for the usage of our system. By fixing these problem, we are able to improve our theoretical model and experiment setup.

摘要 i
Abstract iii
誌謝 v
目錄 vi
圖目錄 viii
第一章 研究動機 1
第二章 簡介 3
2.1 量子相干性(Quantum coherence)與關聯(correlation) 3
2.1.1 單光子（Single photon）與雙光子(biphoton) 3
2.1.2 量子糾纏及並發值(Concurrence) 4
2.1.3 CHSH貝爾不等式（Bell-CHSH inequality） 6
2.1.4 量子可操控性（Quantum steering） 8
2.2 亂流(Turbulence)系統 11
2.2.1亂流系統架構 11
2.2.2 亂流系統的運作模式 15
第三章 量子關聯性實驗與分析方法 17
3.1 亂流（Turbulence）大小判斷依據 17
3.1.1 量子態的建構 17
3.1.2 保真度(Fidelity) 18
3.1.3 純度(Purity) 19
3.2 量子關聯性實驗 20
3.2.1 亂流模式的選擇 20
3.2.2 實驗結果分析 31
第四章 亂流模型優化 40
4.1 光子統計誤差 40
4.2 利用古典參考光 46
4.2.1 以理想作用子還原各別元件 46
4.2.2 轉換矩陣的建立 54
4.2.3 實驗模型還原 59
4.3 量子光優化法 60
第五章 量子通道分析 66
5.1 數學模型 66
5.1.1 不變的糾纏態 67
5.1.2 糾纏態的操控 68
5.2 物理圖像 68
5.2.1 Bloch Sphere上單光子的演化 68
5.2.2 雙光子的糾纏度 71
第六章 結論 74

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