2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/92593The purpose of this paper is to obtain a sufficient and necessary condition as a criteria to test whether an arbitrary multipartite state is entangled or not. Based on the tensor expression of a multipartite pure state, the paper shows that a state is separable iff $| \mathbf{C}(ρ)| $ =0 for pure states and iff $C(ρ)$ vanishes for mixed states.4 pages, 1 figuresQuantum Physicstext