Quantum-state estimation problem via optimal design of experiments

TL;DR

This paper explores optimal experimental designs for quantum-state estimation, focusing on qubit models and comparing various optimality criteria to identify efficient strategies.

Contribution

It introduces a unified framework for optimal design criteria in quantum-state estimation and extends classical theorems to qubit systems.

Findings

D-optimal design is equivalent to a specific A-optimal design in qubit systems.

Optimal designs can vary significantly in efficiency across different criteria.

Explicit comparisons highlight the importance of criterion selection for experimental efficiency.

Abstract

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.