Optimal distributed multi-parameter estimation in noisy environments

Abstract

We consider the task of multiple parameter estimation in the presence of strong correlated noise with a network of distributed sensors. The signals and the noises have different spatial dependence but are encoded with the same local generators. We study how to find and improve noise-insensitive strategies. We show that sequentially probing with GHZ states from the decoherence-free subspace that we identify is asymptotically optimal up to a factor of at most 4 in the limit of many repetitions. The implementation of such strategies only requires local read-out and ‘passive’ resources—an initially entangled state of the sensors and tunable local interaction strength.