Multipartite entanglement in Chern-Simons theory

Compared to the two-qubit case, the qualitative patterns of quantum entanglement exhibit a rich structure in many body systems. Different forms of entanglement have different operational uses: therefore, it is crucial to understand the landscape of multipartite entanglement structures. This is especially true in Chern-Simons theory, whose topological nature protects it from local errors in quantum computing. Utilizing tools from topological and conformal field theory and knot theory, we extend previous classifications of the multipartite entanglement structure in a wide class of "link edge states", whose structure depends only on global, topological features of the geometry defining the state. This class of states spans all three possible types of link states, and so is quite broad. This work has clear applications to topological quantum computing, but may also provide tools for studying multipartite entanglement in other finite dimensional systems.