Abstract: We investigate the problem of quantum remote implementation of a single-qubit rotation operation using three-qubit entangled state. Firstly,we utilize the entanglement property of maximally entangled Greenberger--Horne--Zeilinger (GHZ) state to design a theoretical scheme for implementing the operation remotely with unit fidelity and unit probability. Then, we put forward two schemes for conclusive implementing the non-local single-qubit rotation with unit fidelity by employing a partially entangled pure GHZ state as quantum channel. The features of these schemes are that a third side is included,who may participate the process of quantum remote implementation as a supervisor. Furthermore, when the quantum channel is partially entangled,the third side can rectify the state distorted by imperfect quantum channel.In addition to the GHZ class state, the $W$ class state can also be used to remotely implement the same operation probabilistically. The probability of successful implementation using the $W$ class state is always less than that using the GHZ class state.

Key words: single-qubit rotation, remote implementation, GHZ class state, $W$ class state