  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.
