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    Observing fundamental triple uncertainty relations

    Yan Wang1,2,3,4,*, Jie Zhou5,*, Xing-Yan Fan6, Ze-Yan Hao1,2,3, Jia-Kun Li1,2,3, Zheng-Hao Liu1,2,3, Ya Xiao7, Kai Sun1,2,3,8,†, Jin-Shi Xu1,2,3,8 et al.

    Jing-Ling Chen6,‡, Chuan-Feng Li1,2,3,8,§, and Guang-Can Guo1,2,3,8

    • *These authors contributed equally to this work.
    • †Contact author: ksun678@ustc.edu.cn
    • ‡Contact author: chenjl@nankai.edu.cn
    • §Contact author: cfli@ustc.edu.cn

    Phys. Rev. A 113, 062447 – Published 22 June, 2026

    DOI: https://doi.org/10.1103/4cbk-96qs

    Abstract

    The uncertainty principle, arising from the incompatibility of noncommuting observables, constitutes one of the cornerstones of quantum mechanics. While uncertainty relations involving pairs of observables have been extensively investigated, experimentally accessible tight uncertainty relations for multiple observables in bipartite systems remain largely unexplored. Here, we experimentally investigate tight triple uncertainty relations in two-qubit systems using two physically motivated constructions of angular-momentum operators. On a photonic quantum platform, we formulate and verify both product-form and additive-form triple uncertainty relations associated with the operators J⃗=S⃗1×S⃗2 and K⃗=S⃗1⊗1+1⊗S⃗2. We experimentally observe saturation of the tight bound with high fidelity and verify the universal constant 2/3 for the investigated classes of triple uncertainty relations. Furthermore, we construct optimized uncertainty functions whose maximal values exhibit a monotonic correspondence with entanglement concurrence for Bell-type and Werner-state families. Our results establish an experimentally accessible framework for studying multiobservable uncertainty relations in bipartite quantum systems and provide additional insight into the interplay between measurement incompatibility and quantum entanglement.

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