We develop a method for visualizing the internal structure of multipartite entanglement in pure stabilizer states. Our algorithm graphically organizes the many-body correlations in a hierarchical structure. This provides a rich taxonomy from which one can simultaneously extract many quantitative features of a state including some traditional quantities such as entanglement depth, $k$-uniformity, and entanglement entropy. Our method also presents an alternative computational tool for extracting the exact entanglement depth and all separable partitions of a stabilizer state. Our construction is gauge invariant and goes beyond traditional entanglement measures by visually revealing how quantum information and entanglement is distributed. We use this tool to analyze the internal structures of prototypical stabilizer states (Greenberger-Horne-Zeilinger state, cluster state, stabilizer error correction codes) and are able to contrast the complexity of highly entangled volume law states generated by random unitary operators and random projective measurements.

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• Entanglement entropy
• Entanglement measures
• Open quantum systems & decoherence
• Quantum circuits
• Quantum computation
• Quantum correlations in quantum information
• Quantum correlations, foundations & formalism
• Quantum entanglement
• Quantum error correction
• Quantum information processing
• Quantum information theory
• Quantum measurements
• Shannon entropy
• 1-dimensional spin chains
• 1-dimensional systems
• Non-Hermitian systems
• Quantum many-body systems
• Superconducting qubits