Multipartite entanglement structures in quantum stabilizer states

TL;DR

This paper introduces a visualization method for the internal structure of multipartite entanglement in stabilizer states, revealing detailed correlations and entanglement features beyond traditional measures.

Contribution

The authors develop a hierarchical visualization algorithm that captures complex entanglement structures and provides an alternative computational approach for analyzing stabilizer states.

Findings

Visualizes multipartite entanglement hierarchically

Extracts entanglement depth and separable partitions

Analyzes complexity of volume law states

Abstract

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 (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 operators and random projective measurements.