Controlled Bidirectional Remote Preparation of Single- and Two-Qubit State

We propose two novel schemes for controlled bidirectional remote state preparation of single- and two-qubit state by using five-and nine-qubit entangled state as the quantum channel. First, our schemes are considered in two cases that the coefficients of prepared state are real and complex, respectively. Second, by virtue of appropriate measurement and the corresponding local unitary operations, we explicitly give how to accomplish these preparation tasks. Third, taking the first scheme as an example, we discuss our scheme in four kinds of noisy environments (bit-flip, phase-flip, amplitude-damping and depolarizing noisy environment). We calculate fidelity and find that it depends on the prepared state coefficients and decoherence rate. Eventually, some discussions are given.