Probing many-body Bell correlation depth with superconducting qubits
School of Physics, Zhejiang University（浙江大学物理学院）；Center for Quantum Information, IIIS, Tsinghua University（清华大学信息科学技术研究院量子信息中心）；Instituut-Lorentz, Universiteit Leiden（莱顿大学洛伦兹研究所）；ZJU-Hangzhou Global Scientific and Technological Innovation Center（浙江大学杭州国际科技创新中心）；Hefei National Laboratory（合肥国家实验室）；Shanghai Qi Zhi Institute（上海量子科学研究中心）
Quantum nonlocality describes a stronger form of quantum correlation than that of entanglement. It refutes Einstein's belief of local realism and is among the most distinctive and enigmatic features of quantum mechanics. It is a crucial resource for achieving quantum advantages in a variety of practical applications, ranging from cryptography and certified random number generation via self-testing to machine learning. Nevertheless, the detection of nonlocality, especially in quantum many-body systems, is notoriously challenging. Here, we report an experimental certification of genuine multipartite Bell correlations, which signal nonlocality in quantum many-body systems, up to 24 qubits with a fully programmable superconducting quantum processor. In particular, we employ energy as a Bell correlation witness and variationally decrease the energy of a many-body system across a hierarchy of thresholds, below which an increasing Bell correlation depth can be certified from experimental data. As an illustrating example, we variationally prepare the low-energy state of a two-dimensional honeycomb model with 73 qubits and certify its Bell correlations by measuring an energy that surpasses the corresponding classical bound with up to 48 standard deviations. In addition, we variationally prepare a sequence of low-energy states and certify their genuine multipartite Bell correlations up to 24 qubits via energies measured efficiently by parity oscillation and multiple quantum coherence techniques. Our results establish a viable approach for preparing and certifying multipartite Bell correlations, which provide not only a finer benchmark beyond entanglement for quantum devices, but also a valuable guide towards exploiting multipartite Bell correlation in a wide spectrum of practical applications.
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