Introduction to generation, manipulation and characterization of optical quantum states

TL;DR

This tutorial provides foundational theoretical tools for understanding, generating, manipulating, and measuring optical quantum states, including key devices and measurement techniques like homodyne detection and quantum teleportation.

Contribution

It offers a comprehensive introduction to the theoretical framework and experimental tools for optical quantum state generation, manipulation, and characterization.

Findings

Explains the role of quadrature operators and characteristic functions.

Describes the use of Wigner functions and operator ordering.

Details homodyne detection and tomography techniques.

Abstract

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.