Many-body entanglement: Permutations and equivalence classes
  With an easily applicable criterion based on permutation symmetries of (identically prepared) replicas of quantum states we identify distinct entanglement classes in high-dimensional multi- partite systems. The different symmetry properties of inequivalent states provide a rather intuitive picture of the otherwise very abstract classification of many-body entangled states. 
Florian Mintert, Benno Salwey, Andreas Buchleitner
quant-ph