  Remote state preparation (RSP) provides a useful way of transferring quantum
information between two distant nodes based on the previously shared
entanglement. In this paper, we study RSP of an arbitrary single-photon state
in two degrees of freedom (DoFs). Using hyper-entanglement as a shared
resource, our first goal is to remotely prepare the single-photon state in
polarization and frequency DoFs and the second one is to reconstruct the
single-photon state in polarization and time-bin DoFs. In the RSP process, the
sender will rotate the quantum state in each DoF of the photon according to the
knowledge of the state to be communicated. By performing a projective
measurement on the polarization of the sender's photon, the original
single-photon state in two DoFs can be remotely reconstructed at the receiver's
quantum systems. This work demonstrates a novel capability for long-distance
quantum communication.
