A Note on Local Unitary Equivalence of Isotropic-like States
  We consider the local unitary equivalence of a class of quantum states in bipartite case and multipartite case. The necessary and sufficient condition is presented. As special cases, the local unitary equivalent classes of isotropic state and werner state are provided. Then we study the local unitary similar equivalence of this class of quantum states and analyze the necessary and sufficient condition. 
Tinggui Zhang, Bobo Hua, Ming Li, Ming-Jing Zhao, and Hong Yang
quant-ph