Quantum Tomography twenty years later

TL;DR

This paper reviews twenty years of developments in classical and quantum tomography, presenting a unifying framework and exploring three key areas: line and submanifold tomography, coherent state tomography, and algebraic quantum tomography.

Contribution

It offers a comprehensive conceptual framework unifying various tomography methods and highlights three significant areas demonstrating the scope of classical and quantum tomography.

Findings

Unified mathematical framework for tomography methods

Analysis of tomography along lines and submanifolds

Discussion of coherent state and algebraic quantum tomography

Abstract

A sample of some relevant developments that have taken place during the last twenty years in classical and quantum tomography are displayed. We will present a general conceptual framework that provides a simple unifying mathematical picture for all of them and, as an effective use of it, three subjects have been chosen that offer a wide panorama of the scope of classical and quantum tomography: tomography along lines and submanifolds, coherent state tomography and tomography in the abstract algebraic setting of quantum systems.