Multipartite entanglement structures in quantum stabilizer states

We develop a method for visualizing the internal structure of multipartite entanglement in pure stabilizer states. Our scheme graphically organizes the many-body correlations in a hierarchical structure. This provides a rich taxonomy from which one can extract a number of traditional quantities such as entanglement depth and entanglement entropy. Our construction goes beyond traditional entanglement measures by visually revealing how quantum information and entanglement is internally distributed in a multipartite entangled state. We use this tool to analyze the internal structures of prototypical stabilizer states (GHZ state, cluster state, stabilizer error correction codes) and are able to contrast the complexity of highly entangled volume law states generated by random unitary gates and random projective measurements.