AI 中文总结
研究针对多体贝尔测试在大规模应用的障碍，引入广义Mermin不等式，通过实验在可编程超导处理器上对多达80个量子比特的GHZ态测试，结果表明增加测量设置数可提高贝尔违反率和噪声鲁棒性，为大规模GHZ态提供更优贝尔基准。
AI 中文摘要
多体贝尔测试为量子处理器基准测试提供了仅依赖相关性的途径，但在大规模应用时，受到噪声下多体关联器的快速衰减以及传统贝尔表达式中指数级多项的阻碍。本文引入了具有解析认证界限的有限设置广义Mermin族状态定制贝尔不等式来解决这些可扩展性障碍，其中测量设置数\(m\)提供了与系统大小\(n\)互补的额外认证维度。通过在可编程超导处理器上对多达80个量子比特的Greenberger-Horne-Zeilinger（GHZ）态进行实验测试，结果表明增加\(m\)可提高贝尔违反率和噪声鲁棒性缩放。所有结果仅从测量的关联器和解析界限获得，无需读出校正、层析成像或基于模型的缓解。广义Mermin不等式为有噪声的大规模GHZ态提供了更尖锐的贝尔基准。
英文摘要
Multipartite Bell tests provide a correlation-only route to benchmarking quantum processors, but their application at large scales is hindered by the rapid decay of many-body correlators under noise and exponentially many terms in conventional Bell expressions. Here we address these scalability obstacles by introducing a finite-setting generalized Mermin family of state-tailored Bell inequalities with analytic certification bounds, in which the measurement-setting number $m$ provides an additional certification dimension complementary to the system size $n$. We show that, for the powers-of-two setting choices considered here, increasing $m$ leaves the ideal normalized multipartite quantum value unchanged while lowering the relevant classical bounds, thereby strengthening the Bell-violation ratios and yielding an improved noise-robustness scaling compared to the standard Mermin inequality. We test this construction experimentally on a programmable superconducting processor by preparing Greenberger-Horne-Zeilinger (GHZ) states of up to 80 qubits. Using randomized sampling for direct Bell-operator estimation, we observe Bell ratios that grow exponentially with system size, certify a nonlocality depth of 14, and show that increasing $m$ strengthens both the Bell ratio and depth certification. All results are obtained solely from measured correlators and analytical bounds, without readout correction, tomography, or model-based mitigation. Generalized Mermin inequalities therefore provide a sharper Bell benchmark for noisy large-scale GHZ states.
Comments6 pages, 4 figures; supplemental material: 22 pages
