Werner states can be generalized to the multipartite case. An N -party Werner state is a state that is invariant under U ⊗ ⊗ U ⊗ ⊗ ⋯ ⋯ ⊗ ⊗ U for any unitary U on a single subsystem. The Werner state is no longer described by a single parameter, but by N! − 1 parameters, and is a linear combination of the N! different permutations on N systems.