Cyclic preparation of two-qubit state in two noisy environments

In this paper, a cyclic preparation scheme is proposed. In our scheme, Alice, Bob and Charlie can cyclic prepare two-qubit state with the control of David. Firstly, the quantum channel can be constructed by using H, Z and CNOT operations. And we give the circuit diagram of the construction of the quantum channel and the processing of the scheme. Secondly, the participants perform a single-qubit measurement and three two-qubit measurements through appropriate measurement bases. Moreover, the prepared state can be recovered deterministically and all recovery operations are given. Thirdly, we consider our scheme in two noisy environments (amplitude-damping and phase-damping noisy environment). The fidelities of output states are calculated and the effect factors are discussed. Finally, we give some discussions with other schemes. Our scheme has better communication efficiency because it improves the number of quantum state particles transmitted without increasing the classical communication consumption.