四体双量子系统酉算子的局部不变量

we investigate the local invariants for four-qubit states and seek for some equivalent condition on the local equivalent operators with regard to the action of $SO(4)otimesSO(4)$. In order to find fewer enough invariants, by thinking of the kind of local equivalence as a special case of that with regard to the action of $SO(2^4),$ then we strengthen our result until we find the complete set of the invariants. In addition, we can obtain a result about the case of three extbf{-}qubit quantum system.