Learning Entanglement Quasiprobability from Noisy and Incomplete Data

Quantum Physics [Submitted on 19 Mar 2026] Learning Entanglement Quasiprobability from Noisy and Incomplete Data Yu-Zhuo Li (1), Li-Chao Peng (1, 2, 3), Ke-Mi Xu (1, 2, 3) ((1) MIIT Key Laboratory of Complex-field Intelligent Sensing, School of Optics and Photonics, Beijing Institute of Technology, Beijing, China, (2) Yangtze Delta Region Academy of Beijing Institute of Technology, Jiaxing, China, (3) Center for Photonic Quantum Precision Measurement, Advanced Research Institute of Multidisciplinary Science, Beijing Institute of Technology, Beijing, China) Negativities in quasiprobability distributions, a foundational concept originating in quantum optics, serve as a fundamental signature of quantum nonclassicality, with entanglement quasiprobabilities offering a necessary and sufficient criterion for entanglement. However, practical reconstruction of entanglement quasiprobabilities conventionally requires full quantum state tomography, severely limiting scalability. Here, we propose a deep-learning framework that reconstructs entanglement quasiprobabilities directly from incomplete local projective measurements, bypassing full state reconstruction. Using a residual neural network, partial measurement outcomes are mapped to high-fidelity entanglement quasiprobabilities. Numerical benchmarks up to three qubits show more than a 30\times reduction in reconstruction error compared with state-of-the-art tomographic methods. Experimental validation on photonic entangled states demonstrates reconstruction and entanglement detection with substantially reduced measurement resources. Our results establish machine-learning-assisted reconstruction of entanglement quasiprobabilities as a scalable and practical tool for entanglement characterization in quantum optical systems. Comments: Yu-Zhuo Li and Li-Chao Peng contributed equally. Corresponding authors: Li-Chao Peng (plc@bit.this http URL) and Ke-Mi Xu (xukemi@bit.this http URL) Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.18414 [quant-ph]   (or arXiv:2603.18414v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.18414 Focus to learn more Submission history From: Yuzhuo Li [view email] [v1] Thu, 19 Mar 2026 02:22:07 UTC (3,479 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)