Wigner Function Reconstruction via Deep Generative Models

Po-Hsuan Chen^1*, Tzu-Chia Liu¹, Yu-Chen Lee^1,2, Hong-Bin Chen^1,2,3

¹Department of Engineering Science, National Cheng Kung University, Tainan, Taiwan
²Center for Quantum Frontiers of Research & Technology, National Cheng Kung University, Tainan, Taiwan
³Physics Division, National Center for Theoretical Sciences, Taipei, Taiwan

* Presenter:Po-Hsuan Chen, email:bruce910804@gmail.com

Artificial intelligence (AI) has recently emerged as a powerful tool for quantum-state analysis, providing new approaches to overcome the complexity of non-classicall systems. The Wigner function (WF), which offers a phase-space representation of quantum states, is often difficult to reconstruct experimentally or computationally because of its high dimensionality. In our previous work, we successfully applied deep generative models (DGMs) to reconstruct WFs of fundamental quantum states, including coherent, Fock, and squeezed states, using only a few selected marginals. To further validate the learning capacity and generalization of this framework, we extend it to three more sophisticated physical models: the Jaynes–Cummings model (JCM), the Tavis-Cummings model with two qubits (TJCM) and pair-coherent states (PCS). Synthetic data sets were generated to train DGMs for each case, enabling accurate WF reconstruction even with sparse data. Moreover, the analysis of marginal distributions P(kx), P(ky), and P(ku) reveals deeper insights into coherence and entanglement dynamics. These findings demonstrate that AI-assisted quasi-distribution reconstruction provides an efficient and scalable approach for visualizing quantum states, with potential applications in quantum optics and information science.

Keywords: Wigner function, Deep generative model, Quantum optics, Jaynes Cummings model, Quantum tomography