  We use photon pairs hyperentangled in polarization and orbital angular
momentum to implement a novel entanglement-enhanced quantum state communication
technique, known as SuperDense Teleportation, to communicate a specific class
of single-photon ququart states between two remote parties, with an average
fidelity of 87.0(1)%, almost twice the classical limit of 44%. We compare this
technique with quantum teleportation and remote state preparation and show that
SuperDense teleportation requires less classical information and fewer
experimental resources. We discuss the information content of this constrained
set of states and demonstrate that this set has an exponentially larger state
space volume than the lower dimensional general states with the same number of
state parameters.
