  In previous work the authors introduced a notion of generic states and
obtained criteria for local equivalence of them. Here they introduce the
concept of CHG states maintaining the criteria of local equivalence. This fact
allows the authors to halve the number of invariants necessary to characterize
the equivalence classes under local unitary transformations for the set of
tripartite states whose partial trace with respect to one of the subsystems
belongs to the class of CHG mixed states.
