Genuine (k,m)-Threshold Controlled Teleportation and Multipartite Entanglement

We propose genuine(k,m)-threshold controlling schemes For controlled teleportation via multi-particle entangled states,where the teleportation of a quantum state from a sender(Alice) to a receiver(Bob) is under the control of m supervisors such that k(k≤m) or more of these supervisors can help Bob recover the transferred state. By construction,anyone of our quantum channels is a genuine multipartite entangled state of which any two parts are inseparable.Their properties are compared and contrasted with those of the well-known GHZ,W,and linear cluster states,and also several other genuine multipartite entangled states recently introduced in the literature.