A Characterization For Entangled Vectors

This article presents a simple characterization for entangled vectors in a finite dimensional Hilbert space $H$. The characterization is in terms of the coefficients of an expansion of the vector relative to an orthonormal basis for $H$. This simple necessary and sufficient condition contains a restriction and we also present a more complicated condition that is completely general. Although these characterizations apply to bipartite systems, we show that generalizations to multipartite systems are also valid.