Establishing a quantum communication network would provide advantages in areas such as security and information processing. Such a network would require the implementation of quantum teleportation between remote parties. However, for photonic «qudits» of dimension greater than two, this teleportation always fails due to the inability to carry out the required quantum Bell-state measurement. A quantum communication protocol called Superdense Teleportation (SDT) can allow the reconstruction of a state without the usual 2-photon Bell-state measurements, enabling the protocol to succeed deterministically even for high dimensional qudits. This technique restricts the class of states transferred to equimodular states, a type of superposition state where each term can differ from the others in phase but not in amplitude; this restricted space of transmitted states allows the transfer to occur deterministically. We report on our implementation of SDT using photon pairs that are entangled in both polarization and temporal mode. After encoding the phases of the desired equimodular state on the signal photon, we perform a complete tomography on the idler photon to verify that we properly prepared the chosen state. Beyond our tabletop demonstration, we are working towards an implementation between a space platform in low earth orbit and a ground telescope, to demonstrate the feasibility of space-based quantum communication. We will discuss the various challenges presented by moving the experiment out of the laboratory, and our proposed solutions to make Superdense Teleportation realizable in the space setting.