Correlation additivity relation is superadditive for separable states

Abstract

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.