Control power of a high-dimensional controlled nonlocal quantum computation

We propose a scheme for a high-dimensional nonlocal controlled quantum computation network. A client with limited quantum technology can control a distributed computation between two quantum servers in a secure manner, such that the client's computational information remains private. We define a measure to quantify the client's control power when performing nonlocal quantum gates. We find that, given the same channel resources, the client's control power over nonlocal quantum gate operations between quantum servers is much greater than that of quantum state transfer between quantum servers. Our scheme prevents quantum servers in the network from stealing each other's information or jointly stealing the client's information. Our protocol provides new avenues for building quantum computing networks and methods to develop the resource theory of quantum channels.