Quantum magnetometry with superconducting-qubit Greenberger–Horne–Zeilinger and Dicke probes

Quantum sensing has become a key technology for precision measurement, with applications spanning magnetometry, gravitational sensing, navigation and geodesy, materials and device diagnostics, and biomedical detection. This motivates the study of quantum-enhanced magnetometry with entangled states. We focus on Greenberger–Horne–Zeilinger (GHZ) and Dicke states operated within a Kitaev phase estimation algorithm (PEA). We consider superconducting fluxonium-qubit sensors, which are modelled with relaxation and dephasing noise. Using a Bayesian update procedure, we evaluate the estimation performance and compare the GHZ and Dicke sensors in terms of sensitivity, dynamical range, and information gain. GHZ probes achieve the highest local sensitivity, while Dicke probes maintain comparable sensitivity over a substantially wider bias interval and exhibit improved tolerance to bias errors and edge effects in PEA sequence. Our results demonstrate a trade-off between local peak sensitivity and the achievable dynamical range and robustness under noise.