Optimal distributed multiparameter estimation in noisy environments

We consider the task of multiple parameter estimation in the presence of strong correlated noise with a network of distributed sensors. We study how to find and improve noise-insensitive strategies. We show that sequentially probing GHZ states is optimal up to a factor of at most 4. This allows us to connect the problem to single parameter estimation, and to use techniques such as protection against correlated noise in a decoherence-free subspace, or read-out by local measurements.