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Improved certification of Bell-operator correlations via optimization

Weikang Li1,2,3,*, Mengyao Hu2,3,4,*, Ke Wang5, Shibo Xu5, Zhide Lu6, Jiachen Chen5, Yaozu Wu5, Chuanyu Zhang5, Feitong Jin5 et al.

Xuhao Zhu5, Yu Gao5, Zhengyi Cui5, Aosai Zhang5, Ning Wang5, Yiren Zou5, Fanhao Shen5, Jiarun Zhong5, Zehang Bao5, Zitian Zhu5, Pengfei Zhang7, Hekang Li7, Qiujiang Guo7, Zhen Wang5,8, Dong-Ling Deng1,6,8, Chao Song5,8,†, H. Wang5,7,8, Patrick Emonts2,3,9,10,‡, and Jordi Tura2,3

  • 1Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, China
  • 2Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, the Netherlands
  • 3Applied Quantum Algorithms, Leiden University, 2333 CA Leiden, the Netherlands
  • 4Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
  • 5Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, School of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
  • 6Shanghai Qi Zhi Institute, Shanghai 200232, China
  • 7ZJU-Hangzhou Global Scientific and Technological Innovation Center, Hangzhou, Zhejiang 310027, China
  • 8Hefei National Laboratory, Hefei, Anhui 230088, China
  • 9Institute for Complex Quantum Systems, Ulm University, 89069 Ulm, Germany
  • 10Center for Integrated Quantum Science and Technology, Ulm-Stuttgart, Germany

  • *These authors contributed equally to this work.
  • †Contact author: chaosong@zju.edu.cn
  • ‡Contact author: patrick.emonts@uni-ulm.de
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Phys. Rev. A 114, 042442 – Published 19 October, 2026

DOI: https://doi.org/10.1103/sglx-xq8z

Abstract

Bell nonlocality is an intrinsic feature of quantum mechanics, which can be detected via the violation of Bell inequalities. It is therefore a fundamental question to certify Bell nonlocality from experimental data. Here we present an optimization framework to detect Bell-operator correlations by exploring flexible mappings between Bell inequalities and Hamiltonians corresponding to the Bell operators. We show that several Hamiltonian models can be mapped to new inequalities with improved classical bounds compared to the original one, enabling a more robust certification of Bell-operator correlations. From the other direction, we investigate the mapping from fixed Bell inequalities to Hamiltonians, aiming to maximize quantum violations while considering experimental imperfections. As a practical application, we experimentally exploit this method in an XXZ-like honeycomb-lattice model utilizing over 70 superconducting qubits. The successful application of this technique, together with the combination of the two directions to form an optimization loop, may open new avenues for developing more practical and noise-resilient certification techniques for Bell-operator correlations and enable broader experimental explorations.

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Phys. Rev. A 114, 042442– Published 19 October, 2026
  • Received 7 March 2026
  • Accepted 15 September 2026
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