General controlled cyclic remote state preparations and their analysis

Remote state preparation (RSP) is a method to transfer a known state from a sender to a receiver some distance away. Based on its importance, many kinds of RSP have been proposed in the literature. In this paper, the controlled cyclic RSP protocol is extended to an arbitrary \(n\) $n$ number of parties. To accomplish this goal, two protocols are proposed and compared. The first one is based on a \(2n+1\) $2n+1$ entangled state as a channel, and the other is with \(2n\) $2n$ EPR states. Then, the proposed protocols are analyzed from the controller power’s point of view, and the improved versions are presented. Finally, the protocols have been proposed to send the states with an arbitrary number of qubits. Furthermore, the performance of the protocol is analyzed in the noisy environments.