Mathematical Optics

15	Quantum Memory Channels in Quantum Optics
Tomáš Rybár, Mário Ziman, and Vladimír Bužek

CONTENTS

15.1    Introduction

15.2    Preliminaries

15.2.1  Quantum Channels

15.2.2  Gaussian States and Channels

15.3    Memory Channels and Structure Theorem

15.3.1  Example: Memoryless Channel

15.3.2  Example: Beamsplitter

15.4    Forgetful Channels

15.4.1  Example: Forgetfulness of the Beamsplitter

15.4.2  Example: Non-Forgetful Two-Mode Squeezer

15.5    Finite-Depth Memory Channels

15.6    Summary and Outlook

15.A   Appendix A: Stinespring’s Dilation Theorem

15.B   Appendix B: Structure Theorem

Acknowledgments

References

15.1    INTRODUCTION

Quantum-optical systems have played instrumental role in testing foundations of quantum theory [5,47