An efficient scheme for implementation of multi-qudit parallel control operations on distant audits in quantum network

In a quantum network, it often occurs that there are many remote nodes which should collaborate with each to perform unitary operations. Most of the time, it can be addressed by bi-direction quantum teleportation. However, it often consumes too much quantum resources. In this paper, we propose an efficient scheme for implementation of remote control of some restricted sets of multi-qudit unitary operation. Alice (controller) prepares one cat-like-state by CONT operation and sends them to the remote Bobs (Bob
b
Bob
2
) by sharing Bell channels respectively. Then Bobs perform a series of local operations with cat-like-state's control. By comparing with the previous work, our scheme generalizes it from one controller and one target to one controller and two targets. Our scheme does not only save the working time, but also reduces the quantum communication resources. Moreover, we also give its quantum circuit, which could lead us to a better and clearer understanding. Finally, we generalize our scheme to the case of rf-dimensional qudits.