Multi-hop teleportation of arbitrary multi-qudit states based on d-level GHZ channels

The combination of quantum communication technology and wireless networks brings a flexible and secure communication method that adapts to a more complex and open network environment. A new multi-hop teleportation scheme is investigated for transferring arbitrary unknown multi-qudit states between two distant parties. Based on a more general quantum routing protocol, intermediate nodes are introduced and linked with each other via d-level entangled Greenberger-Horne-Zeilinger states as quantum channels. In this multi-hop teleportation protocol, the source node and all the intermediate nodes can perform the entanglement measurement and transmit the measurement results simultaneously, thus reducing the time consumption largely. Furthermore, a general matrix formula is derived between the measurement results and the receiver's state, which enables the receiver to restore the unknown state efficiently. Compared with previous multi-hop teleportation protocols, the teleportation protocol of arbitrary unknown multi-qudit states of the authors can transfer more information, and it demonstrates lower computational complexity and higher flexibility.