人工智慧（AI）近年來已成為量子態分析和量子資訊研究的重要工具，尤其是在處理非經典量子系統的高維度結構和複雜動力學行為方面。在各種相空間表示中，維格納函數扮演著核心角色，因為它的負區域直接揭示了非經典行為。然而，其高度振盪的結構使得精確重構成為量子態層析成像中一個極具挑戰性的反問題。
在先前研究中，我們已證明深度生成模型（Deep Generative Model, DGM）能夠僅利用有限數量的邊際分布，準確重建數種相對簡單量子態的維格納函數，包括相干態、福克態（Fock states）與壓縮態。這些結果證明了人工智慧輔助的維格納函數重建對於相對簡單的量子系統是可行的。基於此成果，本論文進一步探討一個更具挑戰性的問題：當量子系統具有更豐富的動力學行為與更複雜的非經典相空間結構時，AI 輔助的重建架構是否仍能維持其重建準確性、穩定性與物理一致性。
為了系統地研究這個問題，我們考慮了三個具有代表性的量子態資料集，它們的相空間複雜度逐漸增加。首先，我們引入約化對相干態(RPCS)作為簡單光學態和更複雜的相互作用量子系統之間的中間基準。然後，我們考慮兩個代表性的腔量子電動力學系統：多光子傑恩斯-卡明斯模型（MJCM）和雙原子多光子傑恩斯-卡明斯模型（TMJCM）。約化對相干態提供了相對平滑的約化單模維格納分佈，而MJCM和TMJCM則包含了原子-場耦合、多光子躍遷和糾纏誘導的動力學效應，導致維格納函數具有局域負區域、快速變化的干涉條紋和時變相空間結構。因此，與先前工作中研究的較簡單狀態相比，這些系統為評估所提出的重構模型的學習能力和泛化表現提供了更嚴格的測試案例。
本研究根據維格納函數及其對應邊際分布的解析表示式建立合成資料集，並 使用基於 ResNet 架構的深度生成模型，僅由三組邊際分布 W (x; τ )、W (p; τ ) 與 W (u; τ ) 重建完整的二維維格納函數。此模型透過多個殘差反捲積階段重構 目標維格納函數。此架構的設計目的不僅是學習相空間分布的整體形狀，也在 於捕捉輸入邊際分布與重建準機率結構之間的物理關聯。
數值結果顯示，所提出的 DGM 在分布內（in-distribution）測試，能夠成功重建RPCS、MJCM 與 TMJCM 系統的維格納函數。重構的維格納函數成功地保留了目標態的主要相空間輪廓、負區域和乾涉結構。此外，基於時間演化量子態的分布外（out-of-distribution）測試結果顯示，即使待重建狀態的物理參數位於訓練分布之外，模型仍能捕捉維格納函數的主要動力學特徵。這些結果說明模型並非僅記憶訓練樣本，而是能從稀疏邊際資訊中學習具有物理意義的重建規則。
為了進一步評估所提出的框架，我們也在相同的重建任務下進行了ResNeXt-based 與 diffusion-based 模型的比較研究。結果表明，基於ResNeXt的模型能夠實現與原始基於ResNet的DGM相當的重建性能，而擴散模型則傾向於產生更平滑的相空間分佈，但對局部負區域和精細干涉結構的保留能力較弱。這些結果表明，有效的維格納函數重建不僅取決於模型的複雜度，還取決於其保留具有物理意義的精細尺度特徵的能力。
總結而言，本論文證明基於 ResNet 的深度生成模型能作為一種有效且具有物理意義的維格納函數重建方法，能夠由有限數量的邊際分布重建複雜量子系統的相空間結構。透過將重建任務從相對簡單的量子態延伸至 RPCS、MJCM 與 TMJCM，本研究驗證了 AI 輔助準機率分布重建方法在複雜量子系統中的可行性與擴展性。所提出的框架為量子光學、腔量子電動力學和數據驅動的量子資訊分析等領域的未來應用提供了一種很有前景的人工智慧輔助方法。

Artificial intelligence (AI) has recently become an important tool for quantum-state analysis and quantum information research, particularly for handling the high-dimensional structures and complex dynamics of nonclassical quantum systems. Among phase-space representations, the Wigner function plays a central role because its negative regions directly reveal nonclassical behavior. However, its highly oscillatory structure makes accurate reconstruction a challenging inverse problem in quantum state tomography.
In our previous studies, a deep generative model (DGM) was shown to reconstruct the Wigner functions of relatively simple quantum states, including coherent states, Fock states, and squeezed states, using only a limited number of marginal distributions. These results demonstrated the feasibility of AI-assisted Wigner-function reconstruction for relatively simple quantum systems. Building upon these results, this thesis addresses a more demanding question: whether an AI-assisted reconstruction framework can maintain its accuracy, stability, and physical consistency when applied to quantum systems with significantly richer dynamics and more complicated nonclassical phase-space structures.
To systematically examine this issue, we consider three representative quantum-state datasets with increasing levels of phase-space complexity. First, reduced pair-coherent states (RPCS) are introduced as an intermediate benchmark between simple optical states and more complicated interacting quantum systems. We then consider two representative cavity quantum electrodynamics systems: the multiphoton Jaynes-Cummings model (MJCM) and the two-atom multiphoton Jaynes-Cummings model (TMJCM). The reduced pair-coherent states (RPCS) provide relatively smooth reduced single-mode Wigner distributions, whereas the MJCM and TMJCM include atom-field coupling, multiphoton transitions, and entanglement-induced dynamical effects, leading to Wigner functions with localized negative regions, rapidly varying interference fringes, and time-dependent phase-space structures. Compared with the simpler states investigated in previous work, these systems therefore provide more stringent test cases for evaluating the learning capability and generalization performance of the proposed reconstruction model.
In this work, synthetic datasets are generated from the analytical expressions of the Wigner functions and their corresponding marginal distributions. A ResNet-based deep generative model is then employed to reconstruct the full two-dimensional Wigner function using only three marginal distributions, denoted as W (x; τ ), W (p; τ ), and W (u; τ ). The model reconstructs the target Wigner function through multiple residual deconvolutional stages. This architecture is designed to learn not only the global shape of the phase-space distribution, but also the physical correlation between the input marginals and the reconstructed quasi-probability structure.
The numerical results show that the proposed DGM successfully reconstructs the Wigner functions of the RPCS, MJCM, and TMJCM under in-distribution testing conditions. The reconstructed Wigner functions successfully preserve the major phase-space profiles, negative regions, and interference structures of the target states. Furthermore, out-of-distribution evaluations based on time-evolved quantum states indicate that the model can still capture the main dynamical features of Wigner functions whose physical parameters lie outside the training distribution. These results suggest that the model does not simply memorize training samples, but learns a physically meaningful reconstruction rule from sparse marginal information.
To further evaluate the proposed framework, comparative studies using ResNeXt-based and diffusion-based models are also performed under the same reconstruction task. While the ResNeXt-based model achieves reconstruction performance comparable to that of the original ResNet-based DGM, the diffusion model tends to produce smoother phase-space distributions with weaker preservation of localized negative regions and fine interference structures. These results suggest that effective Wigner function reconstruction depends not only on model complexity, but also on the ability to preserve physically meaningful fine-scale features.
In summary, this thesis demonstrates that the ResNet-based DGM provides an efficient and physically meaningful approach for reconstructing complex Wigner functions from a limited number of marginal distributions. By extending the reconstruction task from relatively simple quantum states to RPCS, MJCM, and TMJCM, this work validates the feasibility and scalability of AI-assisted quasiprobability reconstruction for increasingly complex quantum systems. The proposed framework provides a promising AI-assisted approach for future applications in quantum optics, cavity quantum electrodynamics, and data driven quantum information analysis.

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