Statistical properties of fidelity in quantum tomography protocols in Hilbert spaces of different dimensions

TL;DR

This paper analyzes the statistical properties of fidelity in various quantum tomography protocols, comparing their performance across different Hilbert space dimensions and geometries, to improve quantum state and gate control.

Contribution

It introduces a comprehensive analysis of fidelity in quantum tomography protocols based on symmetric polyhedral geometries, extending understanding across multiple Hilbert space dimensions.

Findings

Protocols based on symmetric polyhedra approach theoretical fidelity limits

Fidelity characteristics vary with Hilbert space dimension and geometry

Results aid in optimizing quantum state and gate control

Abstract

A throughout study of statistical characteristics of fidelity in different protocols of quantum tomography is given. We consider protocols based on geometry of platonic solids and other polyhedrons with high degree of symmetry such as fullerene and its dual polyhedron. Characteristics of fidelity in different protocols are compared to the theoretical level of the minimum possible level of fidelity loss. Tomography of pure and mixed states in Hilbert spaces of different dimension is analyzed. Results of this work could be used for a better control of quantum gates and quantum states in quantum information technologies.