Entanglement criteria based on local uncertainty relations are strictly   stronger than the computable cross norm criterion
  We show that any state which violates the computable cross norm (or realignment) criterion for separability also violates the separability criterion of the local uncertainty relations. The converse is not true. The local uncertainty relations provide a straightforward construction of nonlinear entanglement witnesses for the cross norm criterion. 
Otfried G\"uhne, Matyas Mechler, Geza Toth, Peter Adam