  The positivity of quantum discord is shown to be equivalent to the strong
subadditivity of von-Neumann entropy. This leads us to a necessary and
sufficient condition characterizing the set of states with zero quantum
discord. This also gives us a mathematical definition of pointer states, as
they are the states with zero discord. Finally, we suggest that strong
subadditivity of entropy might delineate the boundaries of the set of quantum
correlations.
