Remote State Preparation via a Non-Maximally Entangled Channel

We investigate remote state preparation (RSP) via a non-maximally entangled channel for three cases: a general qubit, a special ensemble of qubits (qubit states on the equator of the Bloch sphere) and asymptotic limit of N copies of a general state. The results show that the classical communication cost of RSP for the two latter cases can be less than that of teleportation, but for the first case, in a restricted setting, the classical communication cost is equal to that of teleportation. Whether or not this is the case for more general setting is still an open question.