  Understanding the distribution of quantum entanglement over many parties is a
fundamental challenge of quantum physics and is of practical relevance for
several applications in the field of quantum information. Here we use methods
from quantum metrology to microscopically characterize the entanglement
structure of multimode continuous-variable states in all possible
multi-partitions and in all reduced distributions. From experimentally measured
covariance matrices of Gaussian states with 2, 3, and 4 photonic modes with
controllable losses, we extract the metrological sensitivity as well as an
upper separability bound for each partition. An entanglement witness is
constructed by comparing the two quantities. Our analysis demonstrates the
usefulness of these methods for continuous-variable systems and provides a
detailed geometric understanding of the robustness of cluster-state
entanglement under photon losses.
