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Chin. Phys. B, 2026, Vol. 35(7): 070304    DOI: 10.1088/1674-1056/ae0bfd
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An experimental proposal certification for any three-qubit generalized Greenberger-Horne-Zeilinger states based on fine-grained steering inequality

Zhi-Hao Bian(边志浩), Jia-Qi Sun(孙佳琪), and Yi Shen(沈毅)
School of Science, Jiangnan University, Wuxi 214122, China
Abstract  Multi-party quantum steering is an important concept in quantum information theory and quantum mechanics, typically related to quantum entanglement and quantum nonlocality. It enables precise manipulation of large quantum systems, which is essential for large-scale quantum computing, simulations, and quantum communication. Recently, a quantum steering certification for any three-qubit generalized Greenberger–Horne–Zeilinger (GGHZ) state based on the fine-grained steering inequality was proved [Quantum Studies: Mathematics and Foundations 9 175 (2022)]. Here we provide an experimental proposal to prepare the GGHZ state in a photon system. The measurement observables in each party can be realized by different polarization optical elements. By choosing the angles of the waveplates, our experimental proposal can observe the maximum quantum violation for any three-qubit GGHZ state. Our proposal can be easily extended to high-dimensional qubits and multi-photon GHZ states, which provides a method to study the complex multi-party quantum protocols.
Keywords:  quantum steering      generalized GHZ state      fine-grained uncertainty relation  
Received:  08 July 2025      Revised:  16 September 2025      Accepted manuscript online: 
PACS:  03.67.Mn (Entanglement measures, witnesses, and other characterizations)  
  03.65.Ud (Entanglement and quantum nonlocality)  
  03.67.Hk (Quantum communication)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12104186 and 12401597), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20241603), and the Wuxi Science and Technology Development Fund Project (Grant No. K20231008).
Corresponding Authors:  Zhi-Hao Bian     E-mail:  zhihaobian@jiangnan.edu.cn

Cite this article: 

Zhi-Hao Bian(边志浩), Jia-Qi Sun(孙佳琪), and Yi Shen(沈毅) An experimental proposal certification for any three-qubit generalized Greenberger-Horne-Zeilinger states based on fine-grained steering inequality 2026 Chin. Phys. B 35 070304

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