2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/89613We introduce algebraic sets in the products of complex projective spaces for the mixed states in multipartite quantum systems as their invariants under local unitary operations. The algebraic sets have to be the union of the linear subspaces if the state is separable. Some examples are studied based on our criterion10 pages, no figure, minor changes in v2Quantum Physicstext