古典實在性理論無法完全地描述量子狀態，這種量子非實在性已被利用於偵測純然之量子效應，並已被應用於量子資訊處理之中，然而，至今為止還沒有量化量子非實在性的研究方案；本論文先定義一個可被古典實在性理論描述的狀態，並定義一個可使任意狀態轉變成此種狀態的過程，然後以此進一步提出兩種量度來量化量子狀態與過程的量子非實在性，透過這兩種量度，我們整理出任意的量子純態與任意的么正轉換具有最多的量子非實在性，此外，我們研究這兩種量度在量子資訊處理上的應用，例如量測量子通道的量子非實在性以及評估量子邏輯閘的效能，最後，我們亦比較了量子非實在性量度與其他非古典特性的量度，如量子同調性，並指出它們之間的差異性。

Quantum states are not completely described by the classical theory of realism. Such quantum non-realistic features provide tools to detect quantum effects and have applications to quantum information processing. There is, however, no scheme for quantifying non-realistic features. Here we first define a reference state that can be described by the classical realistic theory. A quantum process that changes any states into this reference state is also introduced. We then further propose two measures to quantify the non-realistic features of quantum state and quantum process. With these two novel quantifiers, we show that any pure states and any unitary transformations are the states and the processes of maximal non-realistic features, respectively. Furthermore, we also apply these quantifiers to quantum information processing, such as quantifying non-realistic features of quantum channels and evaluating the performance of quantum gates. Finally, we compare our measures with a quantum coherence quantifier in detail.

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