  In this paper, we study the quantum-state estimation problem in the framework
of optimal design of experiments. We first find the optimal designs about
arbitrary qubit models for popular optimality criteria such as A-, D-, and
E-optimal designs. We also give the one-parameter family of optimality criteria
which includes these criteria. We then extend a classical result in the design
problem, the Kiefer-Wolfowitz theorem, to a qubit system showing the D-optimal
design is equivalent to a certain type of the A-optimal design. We next compare
and analyze several optimal designs based on the efficiency. We explicitly
demonstrate that an optimal design for a certain criterion can be highly
inefficient for other optimality criteria.
