Equivalence of Single-server and Multiple-servers Blind Quantum Computation Protocols

Because quantum computers are expensive, it is envisaged that individuals who want to utilize them would do so by delegating their calculations to someone who has a quantum computer. When quantum computer users delegate computations to quantum servers, they wish to keep information about their calculations hidden from the servers. The protocol of delegating a calculation while hiding information about the calculation from the server is called {\sl blind quantum computation protocol}. Prior research on single-server's blind quantum computation protocol required users to have quantum capabilities. Prior research on multiple-servers' blind quantum computation protocols required users to have just classical capabilities but imposed limits on the server-to-server communication. There are no known single-server blind quantum computation protocols with a classical user and multiple-servers blind quantum computation protocols that allows servers to communicate freely with each other. We show that the existence of these protocols is equivalence.