Comparative analysis of various protocols for high-precision tomography of qudits

TL;DR

This paper compares different quantum tomography protocols for qudits, analyzing their fidelity and efficiency using a universal distribution, to identify optimal methods for high-precision quantum state estimation.

Contribution

It provides a comprehensive comparison of protocols based on symmetric states, MUB, and two-level transformations for qudits of various dimensions.

Findings

Protocols based on symmetric sets and MUB show higher fidelity.

Efficiency varies significantly with qudit dimension.

Universal distribution effectively estimates measurement fidelity.

Abstract

Quantum tomography is an important tool for obtaining information about the quantum state from experimental data. In this study, we conduct a comparative analysis of various quantum tomography protocols, including protocols based on highly symmetric sets of state vectors, on mutually unbiased bases (MUB), and two-level transformations. Using the universal distribution for the fidelity of quantum state tomography, we estimate the fidelity and efficiency of quantum measurements for qudits of various dimensions as applied to a set of random states uniformly distributed over the Haar measure.