Local unitary equivalent consistence for n-party states and their   (n-1)-party reduced density matrices
  We present that the local unitary equivalence of n-party pure states is consistent with the one of their (n-1)-party reduced density matrices. As an application, we obtain the local invariants for a class of tripartite pure qudits. 
Zhen Wang, He-Ping Wang, Zhi-Xi Wang and Shao-Ming Fei
quant-ph