Quantum advantage in distributed sensing with noisy quantum networks

We show that quantum advantage in distributed sensing can be achieved with noisy quantum networks that only distribute noisy entangled states. We derive a closed-form expression of the quantum Fisher information (QFI) for estimating the average of local parameters using Greenberger-Horne-Zeilinger-diagonal probe states, a representative distributed sensing scenario. From the QFI, we obtain the necessary condition to achieve quantum advantage over the optimal local sensing strategy, which can also serve as an optimization-free entanglement detection criterion for multipartite states. We further explore the impacts from imperfect local entanglement generation and local measurement constraint, and our results imply that the quantum advantage is more robust against quantum network imperfections than local operation errors. Notably, these implications still hold when we explicitly consider dephasing during the sensing dynamics. Our results significantly advance the understanding of the achievability of quantum advantage in noisy distributed sensing. They also offer practical guidance for real-world implementation of quantum sensor networks.