Remote State Preparation of qubits Using Quantum Walks in the Presence of Controller

In this paper we describe remote state preparation schemes for a qubit through quantum walks on a line, a cycle and on a two-vertex complete graph. In all these three cases, there is no requirement for shared quantum entangled channels, which precludes the possibility of disturbances created by noisy environments. The state intended for remote preparation, although known to the intender, is not in the physical possession of any of the involved parties. The protocol proposed here is a perfect communication protocol.