Local Unitary Invariants for Multipartite Quantum Systems
  We present an approach of constructing invariants under local unitary transformations for multipartite quantum systems. The invariants constructed in this way can be complement to that in [Science 340 (2013) 1205-1208]. Detailed examples are given to compute such invariant in detail. It is shown that these invariants can be used to detect the local unitary equivalence of degenerated quantum states. 
Jing Wang, Ming Li, Shao-Ming Fei and Xianqing Li-Jost
quant-ph