Visualizing Three-Qubit Entanglement

TL;DR

This paper introduces a graphical geometric framework to visualize and analyze three-qubit entanglement, connecting geometric features with entanglement measures and applying it to physical Hamiltonian states.

Contribution

It develops a novel geometric visualization method for three-qubit entanglement and links it to entanglement measures like the tangle, offering new insights and conjectures.

Findings

Distinct geometric structures correspond to different entanglement classes

Derived bounds relate geometry to entanglement measures

Identified conditions for robust tripartite entanglement in Hamiltonian eigenstates

Abstract

We present a graphical framework to represent entanglement in three-qubit states. The geometry associated with each entanglement class and type is analyzed, revealing distinct structural features. We explore the connection between this geometric perspective and the tangle, deriving bounds that depend on the entanglement class. Based on these insights, we conjecture a purely geometric expression for both the tangle and Cayley's hyperdeterminant for non-generic states. As an application, we analyze the energy eigenstates of physical Hamiltonians, identifying the sufficient conditions for genuine tripartite entanglement to be robust under symmetry-breaking perturbations and level repulsion effects.