Symmetric Dicke States as Optimal Probes for Wave-Like Dark Matter

We identify symmetric Dicke states as the optimal quantum probes for distributed sensing of wave-like dark-matter fields. Within an ensemble-averaged quantum-metrological framework that incorporates the field's random phases and finite coherence, they maximize the Fisher information for short-baseline arrays with $N_d$ sensors and realize a robust $N_d^2$ enhancement. They also retain this collective advantage under amplitude-damping noise, whereas GHZ-type probes are highly fragile and rapidly lose their sensitivity once such noise is included. For two sensors at separations comparable to the dark-matter coherence length, the optimal entangled state acquires an additional spatial-correlation phase and outperforms both Dicke and independent probes. Our framework applies broadly to stochastic bosonic fields, including gravitational waves, and can be implemented with superconducting qubits, atomic ensembles, and NV centers.