  We study the amount of classical communication needed for distributed quantum
information processing. In particular, we introduce the concept of "remote
preparation" of a quantum state. Given an ensemble of states, Alice's task is
to help Bob in a distant laboratory to prepare a state of her choice. We find
several examples of an ensemble with an entropy S where the remote preparation
can be done with a communication cost lower than the amount (2S) required by
standard teleportation. We conjecture that, for an arbitrary N-dimensional pure
state, its remote preparation requires 2log_2 N bits of classical
communication, as in standard teleportation.
