The relation between tangle and local unitary invariants for pure three   and four-qubit states
  A new form of local unitary (LU) transformation invariant is given for multi-qubit states . The general relation between tangle and the LU transformation invariant of pure three and four-qubit states is given. We find that the tangle actually is a special LU transformation invariant. Furthermore, the tangle is a important local unitary (LU) transformation invariant which is a nessesary condition for maximally multi-qubit entangled state. 
Xin-wei Zha, Yun-Guang Zhang, Jian-Xia Qi and Hai-Yang Song
quant-ph