Maximal distant entanglement in Kitaev tube

We study the Kitaev model on a finite-size square lattice with periodic boundary conditions in one direction and open boundary conditions in the other. Based on the fact that the Majorana representation of Kitaev model is equivalent to a brick wall model under the condition $t=\Delta =\mu $, this system is shown to support perfect Majorana bound states which is in strong localization limit. By introducing edge-mode fermionic operator and pseudo-spin representation, we find that such edge modes are always associated with maximal entanglement between two edges of the tube, which is independent of the size of the system.