Simultaneous Detection of High-Dimensional Entanglement for Two Unknown Quantum States

Quantum Physics [Submitted on 21 Mar 2026] Simultaneous Detection of High-Dimensional Entanglement for Two Unknown Quantum States Mao-Sheng Li, Chang-Yue Zhang, Zheng Zheng, Zhihua Chen, Zhen-Peng Xu, Zhihao Ma, Yan-Ling Wang, Shao-Ming Fei, Zhu-Jun Zheng, Otfried Gühne The state overlap, quantified via \tr[\rho \sigma]$\tr[\rho \sigma]$, is a metric widely used to assess the closeness between two quantum states \rho and \sigma. Although global state overlap alone does not directly capture entanglement properties, we uncover that incorporating local state overlaps provide profound insights into the entanglement characteristics of quantum states. To be precise, the ratio of global to local state overlaps provides a lower bound on the Schmidt number, which is usually used for quantifying high-dimensional entanglement. Unlike conventional methods for detecting entanglement, the approach here can simultaneously reveal entanglement information for two unknown quantum states. Moreover, state overlap can be efficiently determined through local randomized measurement methods, which ensures the experimental feasibility of our approach. In a special case, our criterion reduces to an entanglement criterion that is more powerful than the two criteria used most in experiment--the purity criterion and the fidelity-based criterion and also outperform the p_3-PPT method in specific instances. Our findings highlight a promising direction for advancements in entanglement detection experiments. Comments: 15 pages , 4 figures, comments are welcome! Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.20772 [quant-ph]   (or arXiv:2603.20772v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.20772 Focus to learn more Submission history From: Mao-Sheng Li [view email] [v1] Sat, 21 Mar 2026 11:49:35 UTC (1,195 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?)