AI 中文总结
本文提出基于图论的高维量子重叠层析成像，在4×4×2×2光子四体纠缠态上实验实现，用25个设置重构6个两体边际态，揭示分层纠缠结构，提供了可扩展的多维量子系统学习途径。
AI 中文摘要
大规模量子系统通过探索更多粒子与更高维度取得了快速进展，为量子技术发展提供了巨大潜力，但随着局域维度和粒子数增加，其表征变得极为困难。本文基于图论公式提出高维量子重叠层析成像，可高效重构多体高维量子系统的少体边际态。我们在4×4×2×2系统的光子四体纠缠态上完成了实验实现，采用相互无偏基测量，仅用25个投影测量设置就重构了全部6个两体边际态，而所有两体约化态独立层析成像需94个设置，全态层析成像则需225个设置。重构的边际态揭示了对高维量子网络至关重要的分层纠缠结构，进一步表明这些边际态相比基于保真度的判据，能实现对多体高维纠缠更抗噪的认证。本研究为学习多维量子系统提供了可扩展的途径。
英文摘要
Large-scale quantum systems have advanced rapidly via the exploration of more particles and higher dimensions, offering great potential for developing quantum technologies. However, their characterization becomes prohibitive with increasing local dimensionality and particle number. Here we propose high-dimensional quantum overlapping tomography based on a graph-theoretic formulation, which allows one to efficiently reconstruct few-body marginals of multipartite high-dimensional quantum systems. We experimentally realize it on a photonic four-party entangled state in a $4 \times 4 \times 2 \times 2$ system. Using measurements in mutually unbiased bases, we reconstruct all six two-body marginals with only 25 projective measurement settings, compared with 94 and 225 settings for independent tomography of all two-body reduced states and full state tomography, respectively. The reconstructed marginals reveal a layered entanglement structure vital for high-dimensional quantum networks. We further show that these marginals enable more noise-resilient certification of multipartite high-dimensional entanglement than the fidelity-based criterion. Our work thus offers a scalable route for learning multidimensional quantum systems.
