  We quantify and analyze the controller's power in controlled remote state
preparation schemes. Our analysis provides a lower bound on the control power
required for controlled remote preparation of arbitrary D-dimensional states.
We evaluate several existing controlled remote state preparation protocols and
show that some proposed non-maximally entangled channels are not suitable for
perfect controlled remote preparation of arbitrary quantum states from the con-
troller's point of view. We find that for remotely preparing D-dimensional
states, the entropy of each controller should be no less than log_2 D bits. Our
criteria are not only useful for evaluating controlled remote state preparation
schemes but can also be used for other controlled quantum communication
schemes.
