Witness-based nonlinear detection of quantum entanglement

We present a nonlinear entanglement detection strategy that detects entanglement that the linear detection strategy fails. We show that when the nonlinear entanglement detection strategy fails to detect the entanglement of an entangled state with two copies, it may succeed with three or more copies. Based on our strategy, a witness combined with a suitable quantum mechanical observable may detect the entanglement that cannot be detected by the witness alone. Moreover, our strategy can also be applied to detect multipartite entanglement by using the witnesses for bipartite systems, as well as to entanglement concentrations.