Description
Multipartite entanglement provides a refined probe of quantum field theories beyond bipartite measures. We study multipartite entanglement of link states, which are prepared by Euclidean path integral in 3d Chern-Simons theory on manifolds with multiple torus boundaries. For three-component links in Abelian Chern-Simons theory, we present an explicit formula for the Rényi multi-entropy in terms of the linking numbers, which allows an analytic continuation to the multi-entropy. We also discuss the genuine multi-entropy and logarithmic negativity for link states, and show that they admit a clear physical interpretation in the stabilizer-state framework: the genuine multi-entropy quantifies the tripartite entanglement carried by GHZ-type correlations, while the logarithmic negativity captures bipartite entanglement associated with EPR pairs. These results provide a quantitative characterization of multipartite entanglement in topological quantum field theory, with potential connections to quantum anomalies.
