Optimal experiment design revisited: fair, precise and minimal tomography

TL;DR

This paper develops efficient algorithms and analytic solutions for optimal experiment design in quantum state tomography, improving accuracy and bias minimization, with practical validation on qubits.

Contribution

It introduces new numerical and analytic methods for optimal experiment design, including average OED and ODT, and adapts approaches for constrained estimation techniques.

Findings

Algorithms effectively find optimal measurement designs.

Average OED and ODT are generally similar.

Monte-Carlo simulations validate the methods for qubits.

Abstract

Given an experimental set-up and a fixed number of measurements, how should one take data in order to optimally reconstruct the state of a quantum system? The problem of optimal experiment design (OED) for quantum state tomography was first broached by Kosut et al. [arXiv:quant-ph/0411093v1]. Here we provide efficient numerical algorithms for finding the optimal design, and analytic results for the case of 'minimal tomography'. We also introduce the average OED, which is independent of the state to be reconstructed, and the optimal design for tomography (ODT), which minimizes tomographic bias. We find that these two designs are generally similar. Monte-Carlo simulations confirm the utility of our results for qubits. Finally, we adapt our approach to deal with constrained techniques such as maximum likelihood estimation. We find that these are less amenable to optimization than cruder reconstruction methods, such as linear inversion.