二十世紀初期量子力學的興起，從根本上重塑了我們對物理世界的認知，並促成了現代科技的蓬勃發展。正如眾多實驗所證實，量子糾纏（Quantum entanglement）是其迥異於古典物理且最引人入勝的特性之一。此現象代表物理系統間存在一種強大的關聯性，且不受空間距離所限制。目前學界已提出多種應用量子關聯的資訊架構，許多已在實驗上獲得實證。由於光子具有傳播速度快且抗退相干（Decoherence）能力強等特性，尤其在量子通訊與量子成像領域糾纏光子態是極具潛力的資訊載體。

為了辨別量子關聯的嚴格形式，實驗上極需能量測光子系統「非局域性」（Nonlocality）的方法。然而，在實務上精確測量特定的量子性質仍具諸多挑戰與限制。微觀尺度的單光子探測不僅難以達成，且往往需要昂貴的設備。因此，已有研究嘗試利用巨觀尺度的光場強度來估算量子非局域性。

鑑於巨觀測量中的資訊損失可能導致實驗漏洞，本研究透過計算特定光子態的 CHSH 參數，探討此類方法存在的潛在缺陷。我們透過電腦模擬揭示了這些潛在問題，並展示在探測機制使用條件不當的情況下，即使不存在量子關聯，仍可能得到違反貝爾不等式（Bell's inequality）的錯誤結論。最後，我們進一步討論了以光場強度估算光子系統非局域行為的前置條件與系統誤差來源，藉此釐清真正的量子優勢。

The emergence of quantum mechanics in the early 20th century fundamentally reshaped our understanding of the world and stimulated modern technologies. One of the most intriguing features which differ from classical physics, as evidenced by numerous experiments, is quantum entanglement. It is a strong correlation among physical systems and is not constrained in a finite spatial region. Various schemes are proposed to utilize the information capacity of quantum correlation and have already been realized experimentally. Owing to the propagation speed and robustness against decoherence, entangled photonic states are a promising candidate for quantum schemes, especially in quantum communication and quantum imaging.

In order to identify the strong form of quantum correlations, the experimental methods to characterize the nonlocality of photonic systems are demanded. However, a proper measurement of the exact quantum feature is challanging in practice. The detection in the single-photon regime could be difficult to achieve and requires expensive detectors. Therefore, attempts to characterize the nonlocality by intensity detection in a classical regime are made.

Aware of the information loss in a macroscopic measurement which leads to loopholes, we study the potential flaws that may arise in such approach by calculating the CHSH parameter for specific photonic states. We reveal these underlying issues with computer simulations, and showcase a possible situation where Bell inequality is violated without quantum correlation when the detection regime is improperly used. We further discuss the preliminaries and the origin of the systematic errors for the estimation of non-local behavior of photonic systems, and clarify the true quantum advantage.

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