  Casini et al raise the issue that the entanglement entropy in gauge theories
is ambiguous because its definition depends on the choice of the boundary
between two regions.; even a small change in the boundary could annihilate the
otherwise finite topological entanglement entropy between two regions. In this
article, we first show that the topological entanglement entropy in the Kitaev
model which is not a true gauge theory, is free of ambiguity. Then, we give a
physical interpretation, from the perspectives of what can be measured in an
experiement, to the purported ambiguity of true gauge theories, where the
topological entanglement arises as redundancy in counting the degrees of
freedom along the boundary separating two regions. We generalize these
discussions to non-Abelian gauge theories.
