Controlled Teleportation of an Arbitrary Multi-Qudit State in a General Form with d-Dimensional Greenberger–Horne–Zeilinger States

A general scheme for controlled teleportation of an arbitrary multi-qudit state with d-dimensional Greenberger–Horne–Zeilinger (GHZ) states is proposed. For an arbitrary m-qudit state, the sender Alice performs m generalized Bell-state projective measurements on her 2m qudits and the controllers need only take some single-particle measurements. The receiver Charlie can reconstruct the unknown m-qudit state by performing some single-qudit unitary operations on her particles if she cooperates with all the controllers. As the quantum channel is a sequence of maximally entangled GHZ states, the intrinsic efficiency for qudits in this scheme approaches 100% in principle.