  We classify multipartite entanglement in a unified manner, focusing on a
duality between the set of separable states and that of entangled states.
Hyperdeterminants, derived from the duality, are natural generalizations of
entanglement measures, the concurrence, 3-tangle for 2, 3 qubits respectively.
Our approach reveals how inequivalent multipartite entangled classes of pure
states constitute a partially ordered structure under local actions,
significantly different from a totally ordered one in the bipartite case.
Moreover, the generic entangled class of the maximal dimension, given by the
nonzero hyperdeterminant, does not include the maximally entangled states in
Bell's inequalities in general (e.g., in the 4 or more qubits), contrary to the
widely known bipartite or 3-qubit cases. It suggests that not only are they
never locally interconvertible with the majority of multipartite entangled
states, but they would have no grounds for the canonical n-partite entangled
states. Our classification is also useful for that of mixed states.
