A quantitative witness for Greenberger-Horne-Zeilinger entanglement

Along with the vast progress in experimental quantum technologies there is an increasing demand for the quantification of entanglement between three or more quantum systems. Theory still does not provide adequate tools for this purpose. The objective is, besides the quest for exact results, to develop operational methods that allow for efficient entanglement quantification. Here we put forward an analytical approach that serves both these goals. We provide a simple procedure to quantify Greenberger-Horne-Zeilinger-type multipartite entanglement in arbitrary three-qubit states. For two qubits this method is equivalent to Wootters' seminal result for the concurrence. It establishes a close link between entanglement quantification and entanglement detection by witnesses, and can be generalised both to higher dimensions and to more than three parties.This work was funded by the German Research Foundation within SPP 1386 (C.E.), and by Basque Government grant IT-472-10 (J.S.). The authors thank R. Fazio, P. Hyllus, K.F. Renk, and A. Uhlmann for comments, and J. Fabian and K. Richter for their support