Most continuous-variable quantum networks are useful for quantum metrology.*

Distributed quantum sensing is one of the quantum metrological tasks that exploit entanglement to estimate parameters in distant nodes. Until now, it is well known that particular continuous-variable (CV) quantum networks provide enhancement for distributed sensing but it is not clear whether a general quantum network is beneficial. In this work, we investigate the quantum metrological usefulness of typical CV quantum networks. Particularly, we show that most CV quantum networks provide entanglement between modes that enables one to achieve the Heisenberg scaling of an estimation error for distributed quantum displacement sensing, which cannot be attained using product states. Further, we analytically and numerically show that local phase shift operations are essential ingredients for the task. Finally, we find a tolerant photon-loss rate that maintains the quantum enhancement for practical applications.