  In this paper, we study gapped edges/interfaces in a 2+1 dimensional bosonic
topological order and investigate how the topological entanglement entropy is
sensitive to them. We present a detailed analysis of the Ishibashi states
describing these edges/interfaces making use of the physics of anyon
condensation in the context of Abelian Chern-Simons theory, which is then
generalized to more non-Abelian theories whose edge RCFTs are known. Then we
apply these results to computing the entanglement entropy of different
topological orders. We consider cases where the system resides on a cylinder
with gapped boundaries and that the entanglement cut is parallel to the
boundary. We also consider cases where the entanglement cut coincides with the
interface on a cylinder. In either cases, we find that the topological
entanglement entropy is determined by the anyon condensation pattern that
characterizes the interface/boundary. We note that conditions are imposed on
some non-universal parameters in the edge theory to ensure existence of the
conformal interface, analogous to requiring rational ratios of radii of compact
bosons.
