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 [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-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 [Formula: see text]-optimal design which is equivalent to a certain type of the [Formula: see text]-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.
Quantum state smoothing as an optimal Bayesian estimation problem with three different cost functions
