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Understanding the distribution of quantum entanglement over many parties is afundamental challenge of quantum physics and is of practical relevance forseveral applications in the field of quantum information. Here we use methodsfrom quantum metrology to microscopically characterize the entanglementstructure of multimode continuous-variable states in all possiblemulti-partitions and in all reduced distributions. From experimentally measuredcovariance matrices of Gaussian states with 2, 3, and 4 photonic modes withcontrollable losses, we extract the metrological sensitivity as well as anupper separability bound for each partition. An entanglement witness isconstructed by comparing the two quantities. Our analysis demonstrates theusefulness of these methods for continuous-variable systems and provides adetailed geometric understanding of the robustness of cluster-stateentanglement under photon losses.

Characterizing the multipartite continuous-variable entanglement structure from squeezing coefficients and the Fisher information