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    Identifying the three-qubit W state with the quantum uncertainty relation

    Zhi-Jie Liu1, Hao-Nan Qiang1, Jie Zhou2, Mi Xie3, and Jing-Ling Chen1,*

    • 1Theoretical Physics Division, Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, People's Republic of China
    • 2College of Physics and Materials Science, Tianjin Normal University, Tianjin 300382, People's Republic of China
    • 3Department of Physics, School of Science, Tianjin University, Tianjin 300072, People's Republic of China

    • *Contact author: chenjl@nankai.edu.cn

    Phys. Rev. A 113, 062451 – Published 22 June, 2026

    DOI: https://doi.org/10.1103/hn5t-hb29

    Abstract

    The W state, a canonical representative of multipartite quantum entanglement, plays a crucial role in quantum information science due to its robust entanglement properties. Quantum uncertainty relations, on the other hand, form a fundamental cornerstone of quantum mechanics. This work introduces an alternative approach to identifying tripartite W states by leveraging tripartite quantum uncertainty relations. Using a specific set of noncommuting observables, we formulate an uncertainty-based criterion for identifying W states and rigorously demonstrate its generality in distinguishing them from other tripartite entangled states, such as the Greenberger-Horne-Zeilinger state. Our approach bypasses the need for full quantum state tomography, requiring only the verification of a set of uncertainty inequalities for efficient W-state identification. This work provides a theoretical tool for identifying multipartite entangled states and highlights the significant role of quantum uncertainty relations in entanglement characterization.

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