Teleporting a quantum state in a subset of the whole Hilbert space

We investigate the lower bound of the amount of entanglement for faithfully teleporting a quantum state belonging to a subset of the whole Hilbert space. Moreover, when the quantum state belongs to a set composed of two states, a probabilistic teleportation scheme is presented using a non-maximally entangled state as the quantum channel. We also calculate the average transmission efficiency of this scheme.