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Interplay of quantum resources in nonlocality tests

Hai-Hao Dong1,2,3, Yuwei Zhu4,5, Su-Yi Cheng1,2,3, Xingjian Zhang1,2,4, Cheng-Long Li1,2,3, Ying-Zhao Li1,2,3, Hao Li6, Lixing You6, Xiongfeng Ma3,4,* et al.

Qiang Zhang1,2,3,† and Jian-Wei Pan1,2,3,‡

  • *Contact author: xma@tsinghua.edu.cn
  • †Contact author: qiangzh@ustc.edu.cn
  • ‡Contact author: pan@ustc.edu.cn
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Phys. Rev. Research 7, L022055 – Published 5 June, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L022055

Abstract

Nonlocality, evidenced by the violation of Bell inequalities, not only signifies entanglement but also highlights measurement incompatibility in quantum systems. Utilizing the tilted Clauser-Horne-Shimony-Holt (CHSH) Bell inequality, our high-efficiency optical setup achieves a loophole-free violation of 2.0132. This result provides a device-independent lower bound on entanglement, quantified as the entanglement of formation at 0.0159. Moreover, by tuning the parameters of the tilted CHSH inequality, we enhance the estimation of measurement incompatibility, which is quantified by an effective overlap of 4.3883×10−5. To explore the intricate interplay among nonlocality, entanglement, and measurement incompatibility, we generate mixed states, allowing for flexible modulation of entanglement via fast switching among the four Bell states using Pockels cells, achieving a fidelity above 99.10%. Intriguingly, our results reveal a counterintuitive relationship where increasing incompatibility initially boosts nonlocality but eventually leads to its reduction. Typically, maximal nonlocality does not coincide with maximal incompatibility. This experimental study sheds light on the optimal management of quantum resources for Bell-inequality-based quantum information processing.

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Phys. Rev. Research 7, L022055– Published 5 June, 2025
  • Received 9 September 2024
  • Revised 15 January 2025
  • Accepted 28 April 2025
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