Generalized Mermin Inequalities for Benchmarking Large-Scale GHZ States

• URL: http://arxiv.org/abs/2607.23574v1
• Date: Sun, 26 Jul 2026 09:57:14 GMT
• Title: Generalized Mermin Inequalities for Benchmarking Large-Scale GHZ States
• Abstract summary: Multipartite Bell tests provide a correlation-only route to benchmarking quantum processors.<n>Generalized Mermin inequalities provide a sharper Bell benchmark for noisy large-scale GHZ states.
• Score: 13.720001447931956
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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