Abstract: Two schemes for deterministic remotely preparing an arbitrary two-qubit state with complex coefficients using Bell states as the quantum channel are proposed in this work. In the first scheme, the sender can help either one of the two receivers to remotely prepare the original state with the appropriate probability. And in this process, the sender needs to perform three-particle projective measurement and the controller needs to perform Hadamard gate operation. In the second scheme, two senders independently share the classical knowledge of a quantum state, and the receiver can reconstruct the original state if and only if all the senders collaborate with each other. The four-particle projective measurement is needed in this process. It is shown that the total successful probability of the two schemes can reach 1. Moreover, the quantum resource in the two schemes is only the simplest entangled Bell state, and the whole operation process is simple and flexible.

Key words: Bell states channel, arbitrary two-qubit state, deterministic remoter state preparation, controlled remote preparation