物理過程描述了初始態根據過程的特性與規則演化到特定的末態。在量子科技領域裡，像是量子計算中的邏輯閘運算與量子量測等，往往都必須處理過程方面的問題，然而於現實實驗中，可能因環境干擾或實驗上不可預期之因素導致實驗過程不符合預期中的目標量子過程甚至是喪失其非古典特性，因此評估量子過程的品質成為了一個很重要的課題。在本篇論文裡，我們提出了一個全新的古典過程觀念，再進一步結合數值方法開發出廣泛的量化量子過程之工具，且在計算資源可行的情況下，我們的工具可適用於高維度的量子系統。透過這些工具我們可以量化出一個實驗過程中獨特的非古典特性，除此之外，可以屏除掉所有古典模仿的策略並對於任務導向之過程的可靠性提供一個新的指標。利用這些的工具，我們量化了IBM量子電腦的邏輯運算並發現其具有一定的可靠性，而在量子通訊上，這些工具可以反映出量子遙傳上糾纏態的不完美性，且對於三個廣為人知的噪音通道，顯現出這些通道對於噪音強度有著不同的靈敏性，除了上述量子資訊處理的應用外，糾纏態製備中的後選擇過程被我們的工具認定為量子過程，而投影量測過程則被認定為不具有量子特性，另外，在量子狀態的分析上，我們的工具量化出最佳的時態操控性(temporal steerability)。我們的理論對於量子過程提供了一個全新的見解以及量化量子過程研究之參考。

A physical process describes the scenario in which the initial states of objects evolve into specific final states based on the particular rules of the process. Quantum technology, including such fields as quantum computation and quantum measurements, involves many different problems about processes. However, practical processes deviate from the target process, or even lose their nonclassical features, due to environmental interference and/or unexpected experimental conditions. Consequently, the problem of evaluating the quality of practical processes has attracted great interest. This thesis therefore proposes a novel concept of classical processes to develop profoundly wide approaches using numerical methods, and then possibly extend those approaches to high-level system processes. The proposed approaches not only quantify the unique nonclassical features in a given experimental process, but also provide novel benchmarks for the reliability of a task-oriented process via ruling out any classical strategies of mimicry. The quantum computer in IBM Q is quantified and identified as sufficiently quantum by the proposed approaches. For quantum communication, the proposed approaches reveal the imperfection of non-maximal entanglement used as a carrier in quantum teleportation. Moreover, the approaches manifest the different sensitivities of the three well-known noise channels to the noise intensity. Finally, the processes of post-selection used in entanglement generation are shown to be quantum, whereas projective measurements are identified as classical. Regarding the feasibility of the proposed framework for the analysis of states, it is shown that the proposed approaches successfully optimize the temporal steerability. Overall, the framework proposed in this study provides a new insight into quantum-mechanical processes and is thus a useful paradigm for future works aimed at quantifying quantum-mechanical processes.

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