On multipartite invariant states I. Unitary symmetry
  We propose a natural generalization of bipartite Werner and isotropic states to multipartite systems consisting of an arbitrary even number of d-dimensional subsystems (qudits). These generalized states are invariant under the action of local unitary operations. We study basic properties of multipartite invariant states: separability criteria and multi-PPT conditions. 
Dariusz Chruscinski, Andrzej Kossakowski