  We apply the replica trick to compute the entropy of a cylinder amplitude in
string theory. We focus on the contribution from non-perturbative winding modes
and impose tadpole cancellation to understand the correct prescription for
integrating over moduli. Choosing the entangling surface to cut longitudinally
over the whole length of the cylinder, we obtain an answer that is interpreted
as the entropy of a density matrix. We recast this result in target space
language, both in the open and closed string picture.
