Optimal Quantum Estimation with Stabilizer-Based Local Measurements (2508.07150v1)

Abstract: A central challenge in quantum metrology is to identify optimal protocols under measurement constraints that reflect realistic experimental conditions, e.g., local measurements in multipartite scenarios. Here, we present a sufficient criterion for metrological schemes to saturate the quantum Cram\'er-Rao bound (QCRB) using local measurements, based on stabilizer formalism. In ideal settings, we show that graph states always admit local estimation protocols with an optimal estimation precision determined only by the underlying graph structure. A family of graph states is identified as probe states that achieve suboptimal precision scaling. In noisy environments, we construct several subspaces of probe states (mixed in general) that not only saturate the QCRB with local measurements but also maintain approximately invariant precision scaling. These subspaces offer multiple metrological advantages, including high precision, partial noise resilience, and noise-correcting capability prior to parameter encoding. Under dephasing noise, they exhibit markedly better performance than Greenberger-Horne-Zeilinger states. Our results advance the framework for local-measurement quantum metrology, achieving a robust trade-off between precision and noise tolerance.