  We consider remote state preparation protocols for a set of pure states whose
projectors form a basis for operators acting on the input Hilbert space. If a
protocol (1) uses only forward communication and entanglement, (2)
deterministically prepares an exact copy of the state, and (3) does so
obliviously -- without leaking further information about the state to the
receiver -- then the protocol can be modified to require from the sender only a
single specimen of the state. Furthermore, the original protocol and the
modified protocol use the same amount of classical communication. Thus, under
the three conditions stated, remote state preparation requires at least as much
classical communication as teleportation, as Lo has conjectured [PRA 62 (2000)
012313], which is twice the expected classical communication cost of some
existing nonoblivious protocols.
