  Blind quantum computation allows a client with limited quantum capabilities
to interact with a remote quantum computer to perform an arbitrary quantum
computation, while keeping the description of that computation hidden from the
remote quantum computer. While a number of protocols have been proposed in
recent years, little is currently understood about the resources necessary to
accomplish the task. Here we present general techniques for upper and lower
bounding the quantum communication necessary to perform blind quantum
computation, and use these techniques to establish a concrete bounds for common
choices of the client's quantum capabilities. Our results show that the UBQC
protocol of Broadbent, Fitzsimons and Kashefi [1], comes within a factor of 8/3
of optimal when the client is restricted to preparing single qubits. However,
we describe a generalization of this protocol which requires exponentially less
quantum communication when the client has a more sophisticated device.
