Iterative algorithm for the detection and quantification of entanglement

A set of extremal equations for relative entropy E is derived. Solving these equations by means of repeated convergent iterations is shown . The extremal equations indicate that there is a structure of quantum measurement associated with the extremal solution. The separable measurement obtained in this way specifies the extremal separable state and, significantly, provides the optimal entanglement witness operator revealing the possible entanglement of the input states.