  Remote state preparation is the variant of quantum state teleportation in
which the sender knows the quantum state to be communicated. The original paper
introducing teleportation established minimal requirements for classical
communication and entanglement but the corresponding limits for remote state
preparation have remained unknown until now: previous work has shown, however,
that it not only requires less classical communication but also gives rise to a
trade-off between these two resources in the appropriate setting. We discuss
this problem from first principles, including the various choices one may
follow in the definitions of the actual resources. Our main result is a general
method of remote state preparation for arbitrary states of many qubits, at a
cost of 1 bit of classical communication and 1 bit of entanglement per qubit
sent. In this "universal" formulation, these ebit and cbit requirements are
shown to be simultaneously optimal by exhibiting a dichotomy. Our protocol then
yields the exact trade-off curve for arbitrary ensembles of pure states and
pure entangled states (including the case of incomplete knowledge of the
ensemble probabilities), based on the recently established quantum-classical
trade-off for quantum data compression. The paper includes an extensive
discussion of our results, including the impact of the choice of model on the
resources, the topic of obliviousness, and an application to private quantum
channels and quantum data hiding.
