Probabilistic hierarchically controlled teleportation of anarbitrary m -qudit state with a pure entangledquantum channel

Quantum teleportation is a unique quantum information processing method in quantum communication. Researchers have shown considerable interest in hierarchically controlled teleportation by using quantum entangled states as the quantum channel. Protocols for the hierarchically controlled teleportation of an arbitrary single-qubit via a four-qubit χ state and a four-qubit cluster state have been proposed. We present a protocol for the hierarchically controlled teleportation of an arbitrary m -qudit ( d -dimensional quantum system) state by using a partially entangled quantum state as the quantum channel. The sender performs m generalized Bell-state measurements on her 2 m particles. To reconstruct the original state, the upper-grade receiver only needs to apply a unitary operation in accordance with one of the receivers’ measurement results, and the lower-grade receivers need to perform a unitary operation according to all the other receivers’ measurement results. The receivers can reconstruct the original state probabilistically by introducing an auxiliary qubit and performing a collective unitary transformation. The protocol has the advantage of having high channel capacity by using a high-dimensional entangled state as the quantum channel.