  Why do we need quantization to describe vision? What are the quadrature
operators of the electromagnetic field? Is it possible to measure them? What
are the characteristic functions useful for? In this brief tutorial we provide
the theoretical tools needed to describe the generation, manipulation and
characterization of optical quantum states and of the main passive (beam
splitters) and active (squeezers) devices involved in experiments, such as the
Hong-Ou-Mandel interferometer and the continuous-variable quantum
teleportation. We also introduce the concept of operator ordering and the
description of a system by means of the $p$-ordered characteristic functions.
Then we focus on the quasi-probability distributions and, in particular, on the
relation between the marginals of the Wigner function and the outcomes of the
quadrature operator measurement. Finally, we introduce the balanced homodyne
detection to measure the quadrature operator and the homodyne tomography as a
tool for characterizing quantum optical states also in the presence of non-unit
quantum efficiency.
