  We study the local unitary equivalence for two and three-qubit mixed states
by investigating the invariants under local unitary transformations. For
two-qubit system, we prove that the determination of the local unitary
equivalence of 2-qubits states only needs 14 or less invariants for arbitrary
two-qubit states. Using the same method, we construct invariants for
three-qubit mixed states.
  We prove that these invariants are sufficient to guarantee the LU equivalence
of certain kind of three-qubit states. Also, we make a comparison with earlier
works.
