Bidirectional quantum operation teleportation with two four-qubit cluster states

Utilizing two four-qubit cluster states as quantum channel, we propose a bidirectional quantum operation teleportation scheme. In the scheme, by employing only some usual quantum operations, i.e., Pauli operations, two-qubit controlled gate operations and Bell-state measurements, two distant users (partners) can remotely perform their own concerned quantum operation on the partner’s target quantum state, respectively. The impact of two types of fundamental noises (amplitude-damping noise and phase-damping noise) on our scheme is discussed via calculating and analysing its fidelity. Additionally, the scheme can be widely applied in remote control for its outstanding features of determinacy, high efficiency, interactivity, experimental feasibility and easy operability.