Quantum Advantage in Distributed Sensing with Noisy Quantum Networks

It is critically important to analyze the achievability of quantum advantage under realistic imperfections. In this work, we show that quantum advantage in distributed sensing can be achieved with noisy quantum networks which can 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 GHZ-diagonal probe states, an important distributed sensing prototype. 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. In addition, we prove that genuine multipartite entanglement is neither necessary nor sufficient through explicit examples of depolarized and dephased GHZ 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. Finally, we demonstrate that the probe state with potential for quantum advantage in distributed sensing can be prepared by a three-node quantum network using practical protocol stacks through simulations with SeQUeNCe, an open-source, customizable quantum network simulator. Our results significantly advance the understanding of, and offer practical guidance for achieving quantum advantage in distributed sensing under realistic noise.