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 and present necessary and sufficient separability criteria.

• Received 9 January 2006

DOI:https://doi.org/10.1103/PhysRevA.73.062314