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Entanglement thresholds for sequential nonlocality sharing in star networks

Ming-Xiao Li1,2,*, Yuqi Li3,*,†, Rui-Bin Xu1,2,*, Mo-Ran Zhu1,2, Haitao Ma3,‡, Chang-Yue Zhang4,§, and Zhu-Jun Zheng1,2,∥

  • *These authors contributed equally to this work.
  • †Contact author: liyuqi@hrbeu.edu.cn
  • ‡Contact author: hmamath@hrbeu.edu.cn
  • §Contact author: cyzhang@jnu.edu.cn
  • ∥Contact author: zhengzj@scut.edu.cn
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Phys. Rev. Research 8, 033274 – Published 4 September, 2026

DOI: https://doi.org/10.1103/26rt-yvpn

Abstract

Quantum networks promise scalable distributed quantum information processing. Realizing this potential depends critically on the efficient use of nonclassical resources. Sequential sharing of quantum nonlocality provides a resource-efficient route for recycling entanglement across multiple observers. In network settings, however, such recycling is typically constrained by a trade-off between the number of active branches and the achievable sharing depth. Here, we investigate this problem in star networks using probabilistic projective measurements. We establish an explicit entanglement threshold above which nonlocality can be shared across all branches up to any target depth, and below which we determine the optimal trade-off between the number of active branches and the achievable number of sequential rounds. We further analyze the protocol’s robustness to noise and its experimental observability, clarifying its practical feasibility. These results establish quantitative design principles and entanglement requirements for scalable nonlocality recycling in quantum networks.

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Phys. Rev. Research 8, 033274– Published 4 September, 2026
  • Received 20 January 2026
  • Accepted 13 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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