  We present local invariants of multi-partite pure or mixed states, which can
be easily calculated and have a straight-forward physical meaning. As an
application, we derive a new entanglement criterion for arbitrary mixed states
of $n$ parties. The new criterion is weaker than the partial transposition
criterion but offers advantages for the study of multipartite systems. A
straightforward generalization of these invariants allows for the construction
of a complete set of observable polynomial invariants.
