  We deny with a concrete example the generality of the correlation subadditivity relation conjectured by Modi et al's [Phys. Rev. Lett. {\bf 104}, 080501 (2010)] for any quantum state and point out that the correlation additivity relation is actually super-additive for separable states. This work indicates that any effort on explicitly proving the conjecture and finding the subadditivity source is unnecessary and fruitless. 
Correlation additivity relation is superadditive for separable states