Choice of Measurement Sets in Qubit Tomography

TL;DR

This paper investigates how choosing measurement sets based on Platonic solid vertices can enhance the accuracy of qubit state tomography, providing theoretical bounds and simulation results.

Contribution

It introduces a new approach to selecting measurement sets in qubit tomography using Platonic solids, with theoretical bounds and simulation validation.

Findings

Overcomplete measurement sets improve tomography accuracy

Platonic solid measurements provide asymptotic fidelity bounds

Simulations confirm benefits of overcomplete measurement sets

Abstract

Optimal generalized measurements for state estimation are well understood. However, practical quantum state tomography is typically performed using a fixed set of projective measurements and the question of how to choose these measurements has been largely unexplored in the literature. In this work we develop theoretical asymptotic bounds for the average fidelity of pure qubit tomography using measurement sets whose axes correspond to vertices of Platonic solids. We also present complete simulations of maximum likelihood tomography for mixed qubit states using the Platonic solid measurements. We show that overcomplete measurement sets can be used to improve the accuracy of tomographic reconstructions.