Moreover, if ρ ρ 124 is pure, then S ( ρ ρ 2 ) = S ( ρ ρ 14 ) and S ( ρ ρ 4 ) = S ( ρ ρ 12 ) , so the equality holds in the above inequality. Since the extreme points of the convex set of density matrices are pure states, SSA follows from JC;