Mathematical Optics

13	From Classical to Quantum Light and Vice Versa Quantum Phase-Space Methods
Alfredo Luis

CONTENTS

13.1    Quantization

13.1.1  Canonical Quantization

13.1.2  States and Observables

13.1.2.1  Photon Number

13.1.2.2  Phase

13.1.2.3  Quadratures and Homodyne Detection

13.2    Phase-Space Quantization and Dequantization

13.2.1  Introduction

13.2.2  Desirable Properties

13.2.2.1  One to One

13.2.2.2  Proper Marginals

13.2.2.3  Preservation of Simple Functions

13.2.2.4  Reality Equals Hermiticity

13.2.2.5  Preservation of Positivity

13.2.2.6  Good Transformation Properties

13.2.2.7  Comprise Canonical Quantization

13.2.3  Formulation of the Correspondence

13.2.3.1  Quantization and Dequantization Kernels

13.2.3.2  Characteristic Functions ...