Local Invariants for a Class of Tripartite Quantum Mixed States

We study the equivalence of tripartite mixed states under localunitary transformations. The nonlocal properties for a class of tripartite quantum states in${mathbb C}^K otimes {mathbb C}^M otimes {mathbb C}^N$ composite systems are investigated and a complete set of invariants under local unitary transformations for these states is presented. It is shown that two of these states are locallyequivalent if and only if all these invariants have the same values.