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 which 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.

中文翻译：

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通过优化实验设计的量子态估计问题

在本文中，我们研究了优化实验设计框架下的量子态估计问题。我们首先为流行的最优性标准找到任意量子比特模型的最优设计，例如一种-,D-， 和乙- 优化设计。我们还给出了包含这些标准的单参数最优标准族。然后，我们将设计问题的经典结果，即 Kiefer-Wolfowitz 定理，扩展到显示D- 等效于某种类型的最优设计一种- 优化设计。我们接下来根据效率比较和分析几种优化设计。我们明确证明，针对某个标准的最优设计对于其他最优标准可能是非常低效的。