  We calculate the entanglement entropy using a SU(3) quenched lattice gauge
simulation. We find that the entanglement entropy scales as $1/l^2$ at small
$l$ as in the conformal field theory. Here $l$ is the size of the system, whose
degrees of freedom is left after the other part are traced out. The derivative
of the entanglement entropy with respect to $l$ hits zero at about $l^{\ast} =
0.6 \sim 0.7$ [fm] and vanishes above the length. It may imply that the
Yang-Mills theory has the mass gap of the order of $1/l^{\ast}$. Within our
statistical errors, no discontinuous change can be seen in the entanglement
entropy. We discuss also a subtle point appearing in gauge systems when we
divide a system with cuts.
