Joint remote state preparation in multi-hop network under noisy environment

Joint remote state preparation is an important method to transmit quantum information with more senders and higher security. In this paper, we present a deterministic joint remote state preparation scheme in multi-hop network with two senders and N intermediate parties, using only projective measurements and recovery operations. We describe the scheme under the framework of density matrix to investigate the performance of the scheme in noisy environment. The relation of fidelity, noise rate and the number of intermediate nodes is given for three types of noise. It is revealed that the average fidelity attains its minimum when the noise rate is at the most uncertain point, decreases monotonically as the number of intermediate nodes increases. However, in some special cases, the average fidelity of the multi-hop scheme is greater than some existing one step joint remote state preparation scheme.