Experimentally feasible security check for n-qubit quantum secret sharing

In this article we present a general security strategy for quantum secret sharing (QSS) protocols based on the scheme presented by Hillery, Buzek, and Berthiaume (HBB) [Phys. Rev. A 59, 1829 (1999)]. We focus on a generalization of the HBB protocol to n communication parties thus including n-partite Greenberger-Horne-Zeilinger states. We show that the multipartite version of the HBB scheme is insecure in certain settings and impractical when going to large n. To provide security for such QSS schemes in general we use the framework presented by some of the authors [M. Huber, F. Mintert, A. Gabriel, B. C. Hiesmayr, Phys. Rev. Lett. 104, 210501 (2010)] to detect certain genuine n-partite entanglement between the communication parties. In particular, we present a simple inequality which tests the security.