Parallel remote state preparation of arbitrary single-qubit states via linear-optical elements by using hyperentangled Bell states as the quantum channel

It is well known that transmitting quantum states remotely is one of central tasks in quantum information processing. Until now, there are some important works in remote state preparation, the efficient method to transmit quantum states remotely. However, most of them are focused on remote state preparation via one degree of freedom (DOF) of quantum systems. In this article, we investigate the possibility of performing parallel quantum remote state preparation based on two DOFs of photons. We proposed a protocol for parallel remote preparation of arbitrary single-qubit states via hyperentangled photons which are entangled in both spatial-mode DOF and polarization DOF simultaneously. The sender performs unitary operations on his hyperentangled photon according to his knowledge of prepared states; the receiver can reconstruct the original states on his hyperentangled photon if he cooperates with the sender. The scheme has the advantage of having less quantum entanglement cost and classical communication. Moreover, we also discuss the scheme for recursive remote preparation of arbitrary single-qubit states via partially hyperentangled Bell states.