  In quantum teleportation, neither Alice nor Bob acquires any classical
knowledge on teleported states. The teleportation protocol is said to be
oblivious to both parties. In remote state preparation (RSP) it is assumed that
Alice is given complete classical knowledge on the state that is to be prepared
by Bob. Recently, Leung and Shor showed that the same amount of classical
information as that in teleportation needs to be transmitted in any exact and
deterministic RSP protocol that is oblivious to Bob. We study similar RSP
protocols, but not necessarily oblivious to Bob. First it is shown that Bob's
quantum operation can be safely assumed to be a unitary transformation. We then
derive an equation that is a necessary and sufficient condition for such a
protocol to exist. By studying this equation, we show that one qubit RSP
requires 2 cbits of classical communication, which is the same amount as in
teleportation, even if the protocol is not assumed oblivious to Bob. For higher
dimensions, it is still open whether the amount of classical communication can
be reduced by abandoning oblivious conditions.
