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arXiv · 2511.16431

Identifying the $3$-qubit $W$ state with quantum uncertainty relation

Zhi-Jie Liu·Hao-Nan Qiang·Jie Zhou·Mi Xie·Jing-Ling Chen
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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, are a fundamental cornerstone of quantum mechanics. This paper introduces a novel approach to Identifying tripartite $W$ states by leveraging tripartite quantum uncertainty relations. By employing a specific set of non-commuting 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 complete quantum state tomography, as it requires only the verification of a set of uncertainty inequalities for efficient $W$-state identification. This work provides a new theoretical tool for identifying multipartite entangled states and underscores the significant role of quantum uncertainty relations in entanglement characterization.

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Zhi-Jie Liu, Hao-Nan Qiang, Jie Zhou, Mi Xie, Jing-Ling Chen. 2025-11-20. Identifying the $3$-qubit $W$ state with quantum uncertainty relation. https://doi.org/10.1103/hn5t-hb29

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