  A user who does not have a quantum computer but wants to perform quantum
computations may delegate his computation to a quantum cloud server. In order
that the delegation works, it must be assured that no evil server can obtain
any important information on the computation. The blind protocol was proposed
as a way for the user to protect his information from the unauthorized actions
of the server. Among the blind protocols proposed thus far, a protocol with two
servers sharing entanglement, while it does not require to a user any quantum
resource, does not allow the servers to communicate even after the computation.
In this paper, we propose a protocol, by extend this two-server protocol to
multiple servers, which remains secure even if some servers communicate with
each other after the computation. Dummy gates and a circuit modeled after
brickwork states play a crucial role in the new protocol.
