Improved Nonlocality Certification via Bouncing between Bell Operators and Inequalities

Weikang Li; Mengyao Hu; Ke Wang; Shibo Xu; Zhide Lu; Jiachen Chen; Yaozu Wu; Chuanyu Zhang; Feitong Jin; Xuhao Zhu; Yu Gao; Zhengyi Cui; Aosai Zhang; Ning Wang; Yiren Zou; Fanhao Shen; Jiarun Zhong; Zehang Bao; Zitian Zhu; Pengfei Zhang; Hekang Li; Qiujiang Guo; Zhen Wang; Dong-Ling Deng; Chao Song; H. Wang; Patrick Emonts; Jordi Tura

arXiv · 2407.12347

Improved Nonlocality Certification via Bouncing between Bell Operators and Inequalities

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Abstract

Bell nonlocality is an intrinsic feature of quantum mechanics, which can be certified via the violation of Bell inequalities. It is therefore a fundamental question to certify Bell nonlocality from experimental data. Here, we present an optimization scheme to improve nonlocality certification 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 than the original one, enabling a more robust detection of nonlocality. 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 demonstration, we apply this method to an XXZ-like honeycomb-lattice model utilizing over 70 superconducting qubits. The successful application of this technique, as well as combining the two directions to form an optimization loop, may open new avenues for developing more practical and noise-resilient nonlocality certification techniques and enable broader experimental explorations.

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Weikang Li, Mengyao Hu, Ke Wang, Shibo Xu, Zhide Lu, Jiachen Chen, Yaozu Wu, Chuanyu Zhang, Feitong Jin, Xuhao Zhu, Yu Gao, Zhengyi Cui, Aosai Zhang, Ning Wang, Yiren Zou, Fanhao Shen, Jiarun Zhong, Zehang Bao, Zitian Zhu, Pengfei Zhang, Hekang Li, Qiujiang Guo, Zhen Wang, Dong-Ling Deng, Chao Song, H. Wang, Patrick Emonts, Jordi Tura. 2024-07-17. Improved Nonlocality Certification via Bouncing between Bell Operators and Inequalities. https://arxiv.org/abs/2407.12347

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