光子具長距離傳輸等特性，適用於實現如量子通訊與計算之量子資訊處理任務，其中有兩個重要課題: 一，光子傳遞過程中主系統會與環境交互作用，其馬可夫與非馬可夫動力學之探究。二，多光子彼此交互作用、形成光子糾纏，已被視為量子資訊處理重要的資源。針對以上兩項主題，本論文第一部分，我們基於馬可夫動力學定義的完全正可分割性(completely positive divisibility)，從過程觀點提出實驗可行的兩種方法來識別非馬可夫性: 一種為非馬可夫過程穩健性，藉此方法證明非馬可夫性可視為量子過程能力，並定量特徵一個非完全正過程承受最小量完全正操作、成為完全正過程的能力，其中非完全正過程可由量子過程斷層掃描和反矩陣計算得到；另一種是通過準備最少兩個初始態、無需量子過程斷層掃描，有效率地識別非馬可夫動力學；以上兩種方式皆可使用全光學裝置來實現，應用於分析雙折射晶體中單光子與雙光子動力學的非馬可夫性，亦可應用於探索其他非馬可夫動力學系統，如在超導系統中非馬可夫效應的容錯量子計算之估算誤差臨界值。論文第二部份，我們利用II型週期性極化磷酸鈦氧鉀晶體，成功建立薩格納克(Sagnac)干涉儀偏振糾纏光子源；首先，在初步測試階段，將晶體在焦距30公分的聚焦行為下保持在27.1°C，測得單光子產率在輸入功率10.8毫瓦下每秒約58萬個計數；之後將晶體置於無聚焦透鏡的薩格納克干涉儀中，我們測得在輸入功率5毫瓦下每秒約1萬個偏振糾纏光子對，且與最大糾纏貝爾態的保真度優於98%，遠超過CHSH型貝爾不等式古典邊界值達17個標準偏差，已達到相關文獻的糾纏品質。此糾纏光子源可直接應用於量子技術之開發，例如遠程量子態的非古典準備、使用不受信任的實驗裝置完成量子態斷層掃描和通過見證系統的量子同調性展示遠程狀態準備性能等量子資訊處理任務。

Photon has the advantage of long-distance transmission and is suitable for realizing quantum-information processing tasks such as quantum communication and computing. There are two important topics: First, the principal system interacts with the environment during the photon transmission process and the research of its Markovian and non-Markovian dynamics. Second, two photons can interact with each other to form photon entanglement, which has been regarded as an important resource for quantum-information processing. For the above two topics, in the first part of this thesis, we propose two experimentally feasible methods to identify non-Markovianity based on the completely positive (CP) divisibility defined by Markovian dynamics: One is the non-Markovian process robustness, which proves that non-Markovianity can be treated as quantum process capability and quantitatively characterizes the ability of a non-CP process to endure the minimum amount of CP operations to become a CP process, where the non-CP process can be determined by quantum process tomography (QPT) and inverse matrix calculation. The other method is that the identification of non-Markovian dynamics can be efficiently implemented without QPT by preparing a minimum of two initial states. Both of the above methods can be implemented using all-optical devices, which can be applied to analyze the non-Markovianity of single-photon and two-photon dynamics in birefringent crystals and can also be applied to explore other non-Markovian dynamical systems. For example, estimating the error threshold in fault-tolerant quantum computing with non-Markovian effects in superconducting systems. In the second part of the thesis, we successfully established a Sagnac interferometer polarization-entangled photon source by using type-II periodically poled potassium titanyl phosphate (ppKTP); first, in the preliminary testing, the crystal is kept at 27.1°C under the focusing behavior of the 30 cm focal length, and the single-photon yield is measured to be about 580,000 counts per second at the input power of 10.8 mW; the crystal is then placed in a Sagnac interferometer without a focusing lens. We measure about 10,000 polarization-entangled photon pairs per second at the input power of 5 mW with better than 98% fidelity to the maximally entangled Bell state and violate the CHSH-type Bell's inequality by more than 17 standard deviations, has achieved the quality of entanglement in related research. This entangled photon source can be used to implement the quantum-information processing tasks of nonclassical preparation of quantum remote states, quantum state tomography using untrusted devices, and demonstrating remote state preparation performance through witnessing quantum coherence of the system.

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