Eur. Phys. J. Special Topics 203, 3-24 (2012)
https://doi.org/10.1140/epjst/e2012-01532-4

Review

Quantum optics in the phase space

A tutorial on Gaussian states

¹ Dipartimento di Fisica, Università degli Studi di Trieste, 34151 Trieste, Italy
² CNISM UdR Milano Statale, 20133 Milano, Italy

^a e-mail: stefano.olivares@ts.infn.it

Received: 13 January 2012
Revised: 21 February 2012
Published online: 11 April 2012

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.