2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/91157We 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.12 pages. Version 3: minor correctionsQuantum Physicstext