量子科技為當代新興且迅速發展之領域，隨著技術日益成熟，其潛力與優勢逐漸展現於各項應用中。例如，量子計算中的 Shor 演算法可快速進行質因數分解，量子感測技術則能以高精度干涉儀測量重力波，此外，量子模擬亦可應用於複雜環境之模擬分析。然而，量子技術帶來突破的同時，也對既有系統造成挑戰。尤以通訊安全為例，傳統加密系統面臨量子計算所帶來的潛在解密風險，如何在既有設備下建立兼具安全與效率的新型通訊架構，成為重要課題。
有趣的是，這些因量子科技發展而產生的問題，也可由量子技術本身獲得解方。正如量子計算可能破解傳統加密，但量子通訊的出現，則開啟了無法被竊聽的安全通訊新篇章。透過量子金鑰分配（Quantum Key Distribution, QKD），可實現理論上無法攔截的機密傳輸，進一步提升通訊安全之極限。

本論文研究內容可分為兩大部分。第一部分為藉由控制鋰鈮酸鹽（LiNbO₃, LN）晶體的結構設計，透過參數下轉換（Spontaneous Parametric Down-Conversion, SPDC）產生在頻率域上呈現梳狀分布的糾纏光子對，期望藉此提升通訊中每對光子可承載之資訊量。第二部分則重建量子態之密度矩陣並針對外在環境因子造成之擾動進行模擬與分析，探討其對糾纏光子態的影響程度。
根據模擬結果，我們成功產生預期之頻率梳狀糾纏光子對，同時優化產生效率，並藉由溫度調控改變光子對頻譜位置，進一步進行 Hong-Ou-Mandel（HOM）干涉實驗模擬，重建糾纏態的密度矩陣，最後引入相位擾動進行分析。

Quantum technology is a fast-growing and promising field. As the technology develops, its advantages are becoming more apparent in many areas. For example, Shor’s algorithm in quantum computing can factor large numbers quickly, quantum sensing can detect gravitational waves with high precision, and quantum simulation helps us study complex systems. However, these advances also create new challenges for current systems. One major issue is communication security: classical encryption methods may be broken by quantum computers. So, building new systems that are both secure and practical has become an important goal.

Interestingly, some of these problems can also be solved using quantum technologies. While quantum computers can break traditional encryption, quantum communication opens up new ways to transmit information securely. Quantum Key Distribution (QKD), for instance, allows the sharing of secret keys in a way that cannot be eavesdropped, offering a new level of communication security.

This thesis includes two main parts. The first part focuses on generating entangled photon pairs that form a frequency comb using a specially designed lithium niobate (LiNbO₃) crystal and spontaneous parametric down-conversion (SPDC). This can increase how much information each photon pair can carry. The second part focuses on reconstructing the density matrix of the quantum state and simulating how external disturbances affect it.

Our simulations show that we successfully generated the desired frequency-comb entangled photons and improved the generation efficiency. By adjusting the temperature, we shifted the photons’ spectra and simulated Hong-Ou-Mandel (HOM) interference to reconstruct the quantum state's density matrix. Finally, we studied how phase disturbances affect the coherence and purity of the state.

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