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.

Figure 1

Diagram showing client's (Charlie's) controlled participation in nonlocal quantum gates. Alice and Bob are two quantum servers with quantum computers, and they can execute local two-qudit unitary operation on their qudits. The three blue discs connected with dotted lines represent the tripartite ($abc$) entangled quantum channel. Alice and Bob can also send and receive classical information through classical channels. Qudits $A$ and $B$ represent the quantum memory units which can perform quantum computing.

Figure 2

Control power of three different high-dimensional channels as a function of the dimension parameter $d$ ($2\le d\le 12$). (a) $P=1-\frac{2}{d+1}$ is the control power for a controlled nonlocal CP gate with the channel ${|\psi \rangle }_{abc}$ (the red solid line) which is equal to the control power $P_s$ of controlled state teleportation with the channel ${|\psi \rangle }_{abc}$ (the black dotted line). (b) $P^{\prime }=1-\frac{3+d}{{(d+1)}^2}$ is the control power for a controlled nonlocal CP gate with the channel $|{\psi }^{\prime }{\rangle }_{abc}$ (the red solid line) which is larger than the control power $P_s^{\prime }=P_s$ of controlled state teleportation with the channel $|{\psi }^{\prime }{\rangle }_{abc}$ (the black dotted line). (c) $P^{″}=1-\frac{4}{{(d+1)}^2}$ is the control power for a controlled nonlocal CP gate with the channel $|{\psi }^{″}{\rangle }_{abc}$ (the red solid line) and $P_s^{″}=\frac{d-1}{d}$ is the control power of controlled state teleportation with the channel $|{\psi }^{″}{\rangle }_{abc}$ (the black dotted line).