Determining lower bounds on a measure of multipartite entanglement from   few local observables
  We introduce a method to lower bound an entropy-based measure of genuine multipartite entanglement via nonlinear entanglement witnesses. We show that some of these bounds are tight and explicitly work out their connection to a framework of nonlinear witnesses that were published recently. Furthermore we provide a detailed analysis of these lower bounds in the context of other possible bounds and measures. In exemplary cases we show that only a few local measurements are necessary to determine these lower bounds. 
Jun-Yi Wu, Hermann Kampermann, Dagmar Bru{\ss}, Claude Kl\"ockl and   Marcus Huber
quant-ph