Joint remote state preparation (JRSP for short) can reduce the risk brought by one dishonest sender in remote state preparation. Unlike previous protocols that focused on JRSP under memoryless noise channels, in this paper, we study the performance of a deterministic joint remote state preparation scheme under two successive uses of Pauli channels with memory. We give general formulas quantifying the fidelity under the correlated Pauli channels. Specifically, we find that the performance of the protocol is enhanced in the correlated Pauli channel with partial memory. It means that the memory in this kind of noise channels can improve the communication efficiency of JRSP definitely.

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.

Joint remote state preparation (JRSP) has gained much attention since its first appearance. However, almost all the proposals have focused on the JRSP of pure states. In this paper, we present a scheme of JRSP for mixed states via the three-qubit GHZ state. The scheme is deterministic for real coefficient mixed states and probabilistic for complex ones. The corresponding quantum circuits are given for the deterministic JRSP schemes. The model of the deterministic JRSP scheme is introduced in the language of density operators. Furthermore, we investigate the efficiency of deterministic JRSP when some qubits in the protocol are subjected to a noisy environment. Four types of noise usually encountered in quantum communication are considered, i.e. the bit-flip, phase-flip (phase-damping), depolarizing and amplitude-damping noise. We find that the fidelity is affected by both coefficients of the target mixed state and noise parameter of the channel. Specifically, the fidelity decreases with the purity parameter in the presence of noise.

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