  We examine the entanglement properties of the Yang-Mills theory by
calculating $\alpha$ entanglement entropy with $\alpha=2$ using a SU(3)
quenched lattice gauge simulation both in the confinement and the deconfinement
phases. In the confinement phase, the derivative of the $\alpha$ entropy with
respect to the size $l$ of the subregion, whose entanglement properties are
interested in, scales as $1/l^3$, and a clear discontinuity cannot be found
within our statistical errors. The $\alpha$ entropy in the deconfinement phase
saturates at large $l$. The saturation value is comparable with the thermal
entropy of the pure Yang-Mills theory, indicating that the $\alpha$ entropy
obeys the volume law at large $l$ in the deconfinement phase.
