Quantum Teleportation and Entanglement E-Book

Akira Furusawa

• Herausgeber: Wiley-VCH
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch
• Veröffentlichungsjahr: 2011

Seitenzahl: 554

Beschreibung

Unique in that it is jointly written by an experimentalist and a theorist, this monograph presents universal quantum computation based on quantum teleportation as an elementary subroutine and multi-party entanglement as a universal resource. Optical approaches to measurement-based quantum computation are also described, including schemes for quantum error correction, with most of the experiments carried out by the authors themselves. Ranging from the theoretical background to the details of the experimental realization, the book describes results and advances in the field, backed by numerous illustrations of the authors' experimental setups. Aimed at researchers, physicists, and graduate and PhD students in physics, theoretical quantum optics, quantum mechanics, and quantum information.

Leseprobe

Contents

Cover

Half Title page

Related Titles

Title page

Copyright page

Preface

Part One: Introductions and Basics

Chapter 1: Introduction to Quantum Information Processing

1.1 Why Quantum Information?

1.2 States and Observables

1.3 Unitaries

1.4 Non-unitaries

1.5 Entanglement

1.6 Quantum Teleportation

1.7 Quantum Communication

1.8 Quantum Computation

1.9 Quantum Error Correction

1.10 Experiment: Non-optical Implementations

Chapter 2: Introduction to Optical Quantum Information Processing

2.1 Why Optics?

2.2 Quantum Optical States and Encodings

2.3 Quantum Optical Unitaries

2.4 Gaussian Unitaries

2.5 Quantum Optical Non-unitaries

2.6 Gaussian Non-unitaries

2.7 Linear Optics: Possibilities and Impossibilities

2.8 Optical Quantum Computation

Part Two: Fundamental Resources and Protocols

Chapter 3: Entanglement

3.1 Qubit Entanglement

3.2 Qumode Entanglement

Chapter 4: Quantum Teleportation

4.1 Qubit Quantum Teleportation

4.2 Qumode Quantum Teleportation

Chapter 5: Quantum Error Correction

5.1 The Nine-Qubit Code

5.2 The Nine-Qumode Code

5.3 Experiment: Quantum Error Correction

5.4 Entanglement Distillation

5.5 Experiment: Entanglement Distillation

Part Three: Measurement-Based and Hybrid Approaches

Chapter 6: Quantum Teleportation of Gates

6.1 Teleporting Qubit Gates

6.2 Teleporting Qumode Gates

Chapter 7: Cluster-Based Quantum Information Processing

7.1 Qubits

7.2 Qumodes

Chapter 8: Hybrid Quantum Information Processing

8.1 How to Create Non-Gaussian States, Cat States

8.2 Experiment: Creation of Non-Gaussian States, Cat States

8.3 Hybrid Entanglement

8.4 Hybrid Quantum Teleportation

8.5 Hybrid Quantum Computing

References

Index

Akira Furusawa and Peter van Loock

Quantum Teleportation and Entanglement

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The Authors

Prof. Akira FurusawaThe University of TokyoDepartment of Applied PhysicsTokyo, [e-mail]

Dr. Peter van LoockPhysik Institut LS für OptikInstitut Theorie IUniversität Erlangen-NürnbergMax-Planck-Institut (MPL)Erlangen, [e-mail]

All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

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British Library Cataloguing-in-Publication Data:A catalogue record for this book is available from the British Library.

Bibliographic information published by the Deutsche NationalbibliothekThe Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.d-nb.de.

© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany

All rights reserved (including those of translation into other languages). No part of this book maybe reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.

Cover Design Adam Design, Weinheim

ISBN 978-3-527-40930-3

Preface

The field of quantum information processing has reached a remarkable maturity in recent years with regard to experimental demonstrations. In particular, towards an extension of optical communications from the classical into the quantum realm, many proof-of-principle experiments were performed including the generation and distribution of photonic entangled states over free-space or fiber channels. As an application, unconditionally secure quantum key distribution systems have emerged and even developed into a commercially available technology.

Light systems, apart from their obvious usefulness for communication, have now as well turned out to be a serious contender for approaches to quantum computation. A breakthrough in this context was the theoretical discovery of so-called measurement-based models: quantum algorithms no longer depend on sequences of reversible quantum gates, each enacted through well controlled interactions between, for instance, two or more qubits; instead, sequences of measurements on parts of an entangled resource state prepared prior to the computation will do the trick. In other words, quantum entanglement, already known to be a universal resource for quantum communication in conjunction with quantum teleportation, represents a universal resource for quantum computation too – and again the exploitation of the entangled resource relies upon quantum teleportation which, in its ultimate form, achieves arbitrary quantum state manipulations.

The aim of this book is to give a fairly general introduction to two complementary approaches to quantum information processing: those based upon discrete-variable “qubit” systems and those utilizing quantum oscillator systems (“qumodes”) most naturally represented by continuous quantum variables such as amplitude and phase. In quantum optics, the corresponding photonic systems would consist of just a few photons or they would correspond to fields with extremely high mean photon numbers, respectively. The qubit may then be represented by the polarization of a single photon, while a qumode state is encoded into an infinite-dimensional phase space. Entangled states can be defined, formulated, and experimentally realized in either dimension, including their use for quantum teleportation. Since either approach encounters somewhat different complications when it comes to more sophisticated quantum information protocols, a recent trend in optical quantum information is to combine the two approaches and to exploit at the same time discrete and continuous degrees of freedom in a so-called hybrid fashion. From a more physical point of view, one could say that in an optical hybrid protocol both the wave and the particle properties of light are exploited simultaneously. Sometimes people would use a more general definition for “hybrid systems”, namely any combined light-matter systems. In our quantum optical context, the two definitions would coincide when the matter system consists of atomic spin particles and the light system is described by continuous quantum variables –- a fairly natural scenario.

In the first part of the book, an introduction to the basics of quantum information processing is given independent of any specific realization, but with an emphasis on the two complementary qubit and qumode descriptions. The second chapter of part I then specifically refers to optical implementations. While this first part of the book is mainly theoretical, parts II and III contain detailed descriptions of various experiments. Those specific sections on experiments are each indicated by “experiment:” throughout. One can easily infer from the table of contents that the frequency of experimental sections increases with each chapter of the book. The in some sense unifying formalism for the qubit and qumode approaches is the so-called stabilizer formalism which is therefore used in various sections throughout the book starting from the introductory sections. Summary boxes of the most important formulas and definitions have been included throughout the first three chapters of the book in order to make the introductory parts more comprehensible to the reader.

We hope this book will convey some of the excitement triggered by recent quantum information experiments and encourage both students and researchers to (further) participate in the joint efforts of the quantum optics and quantum information community.

November 2010

Akira Furusawa andPeter van Look

Part One

Introductions and Basics