Quantum optics in the phase space - A tutorial on Gaussian states

TL;DR

This tutorial explains the phase-space description of Gaussian states in quantum optics, covering their mathematical tools, manipulation, evolution, and characterization for quantum information applications.

Contribution

It provides a comprehensive introduction to the phase-space methods for Gaussian states, emphasizing their relevance in quantum information processing.

Findings

Gaussian states are characterized by Gaussian Wigner functions.

Phase-space methods facilitate manipulation and analysis of Gaussian states.

Application of Gaussian states in quantum information is highlighted.

Abstract

In this tutorial, we introduce the basic concepts and mathematical tools needed for phase-space description of a very common class of states, whose phase properties are described by Gaussian Wigner functions: the Gaussian states. In particular, we address their manipulation, evolution and characterization in view of their application to quantum information.