Abstract
By quantifying the difference between quantum mutual information through weak measurement performed on a subsystem one is led to the notion of super quantum discord. The super version is also known to be difficult to compute as the quantum discord which was captured by the projective (strong) measurements. In this paper, we give effective bounds of the super quantum discord with or without phase damping channels for higher-dimensional bipartite quantum states, and found that the super version is always larger than the usual quantum discord as in the 2-dimensional case.