Quantum Communications in New Telecommunications Systems E-Book

Malek Benslama

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 244

Veröffentlichungsjahr: 2017

Beschreibung

Quantum Communications in New Telecommunications Systems Computers are quickly making the transition from silicon towards miniaturization, which now risks reaching its limits as dictated by the laws of physics. Quantum communications are the answer to post-silicon computers. The main applications for quantum communications in the domain of telecommunications are beginning to appear, with some commercial applications already on the market. This book explores the technological advances in quantum communications with a special focus on telecommunications systems. The authors provide a comprehensive state of the art on quantum communications and quantum signal processing. The reader will learn about the advantages, current applications and future prospects of quantum technology.

Leseprobe

Table of Contents

Cover

Dedication

Title

Copyright

Foreword

Preface

Introduction

1 The State of the Art in Quantum Communications

1.1. Quantum mechanics as a generalized probability theory

1.2. Contextuality

1.3. Indeterminism and contextuality

1.4. Contextuality and hidden variables

1.5. Non-locality and contextuality

1.6. Bell states

1.7. Violation of the Leggett–Garg inequality

1.8. Violation of the Bell inequality

1.9. EPR paradox

2 Concepts in Communications

2.1. Quantum limits

2.2. Qubits

2.3. Qudit and qutrit

2.4. Pauli matrices

2.5. Decoherence

2.6. Entanglement

3 Quantum Signal Processing

3.1. Wigner distribution

3.2. Quantum Fourier transform

3.3. Gauss sums in a quantum context

3.4. Geometry for quantum processing

4 Quantum Circuits

4.1. Reversible logic

4.2. Reversible circuits

4.3. Quantum gates

4.4. Toffoli gate

4.5. Deutsch gate

4.6. Quantum dots

4.7. QCA

5 Optical Fibers and Solitons

5.1. Introduction

5.2. Optical fibers

5.3. Soliton solutions for differential equations

5.4. Conclusion

6 Photonic Crystals

6.1. General introduction

6.2. Photonic crystals

6.3. Three-dimensional photonic crystals

6.4. Filters and multiplexors

6.5. Add-drop filters

6.6. Digital methods for photonic crystal analysis

6.7. Conclusion

7 ROADM

7.1. Technological advances

7.2. “Router”-type filter

8 WDM

8.1. Operating principle

8.2. Using WDM systems

8.3. DWDM networks

9 Quantum Algorithms

10 Applications

10.1. Laser satellites

11 Quantum Cryptography

11.1. Cloning photons

11.2. Quantum cryptography

11.3. Solutions to the practical limits of quantum cryptography

11.4. Quantum error correcting codes

Conclusion

Bibliography

Index

End User License Agreement

List of Tables

2 Concepts in Communications

Table 2.1. Average qudits levels

4 Quantum Circuits

Table 4.1. Truth table of Toffoli gate

Guide

Cover

Table of Contents

Begin Reading

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To our mother, with profound gratitude and affection.

– Malek Benslama, Achour Benslama

Series EditorGuy Pujolle

Quantum Communications in New Telecommunications Systems

Malek Benslama

Achour Benslama

Skander Aris

First published 2017 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd 27-37 St George’s RoadLondon SW19 4EUUK

www.iste.co.uk

John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USA

www.wiley.com

© ISTE Ltd 2017

The rights of Malek Benslama, Achour Benslama and Skander Aris to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 9781848219908

British Library Cataloguing-in-Publication DataA CIP record for this book is available from the British LibraryISBN 978-1-84821-990-8

Foreword

Four books devoted solely to satellite communications: this is the challenge set by Professor Malek Benslama of the University of Constantine, who understood that a new discipline was in the process of taking shape.

He demonstrated this by organizing the first International Symposium on Electromagnetism, Satellites and Cryptography in Jijel, Algeria in June 2005. The success the congress enjoyed, surprising for a first event, shows that there was a need to gather, in a single place, specialists in skills that were sometimes much removed from one another. The 140 accepted papers covered systems for electromagnetic systems as well as circuit and antennae engineering and cryptography, which is very often based on pure mathematics. Synergy between these disciplines is necessary to develop the new field of activity that is satellite communication.

The emergence of new disciplines of this type has been known in the past: for electromagnetic compatibility, it is as necessary to know electrical engineering for “driven modes” and “choppers” as electromagnetics (“radiating modes”) and to be able to define specific experimental protocols. Further back in time, we saw the emergence of computing, which, at the start, lay in the field of electronics and was able, in the course of time, to become independent.

Professor BenSlama has the outlook and open-mindedness indispensable for bringing to fruition the synthesis between the skills that coexist in satellite telecommunications. I have known him for 28 years and for me it is a real pleasure to remember all these years of close acquaintance. There has not been a year in which we have not had an opportunity to see one another. First, for 15 years, he worked on the interaction between acoustic waves and semiconductors. He specialized in resolving piezoelectric equations (Rayleigh waves, creeping waves, etc.), and, at the same time, he was interested in theoretical physics. A doctoral thesis in engineering and then a state thesis crowned his professional achievements. Notably, his examination committee included Madame HENAF, then Chief Engineer for the National Center for Telecommunications Studies. He was already interested in telecommunications, but also, with the presence of M. Michel Planat, responsible for research at CNRS, in the difficult problem of synchronizing oscillators.

It is with Michel Planat that he developed the way that will lead to quantum cryptography. He made this transformation over 10 years, thus moving without any apparent difficulty from Maxwell’s equations to Galois groups. He is now therefore one of the people most likely to dominate all those diverse disciplines that form satellite telecommunications.

I wish, with all my friendly admiration, that these four monographs meet with a warm welcome from students and teachers.

Emeritus Professor Henri BAUDRANDENSEEIHT Toulouse

Preface

This book follows on from three other books published by ISTE [BEN 15, BEN 15, BEN 16]. I would like to express my respect and gratitude for this publishing house, which makes a decisive contribution to the publishing and distribution of French-speaking scientific authors. I could not forget Professor Guy Pujolle, Director of the Networks and Telecommunications Series, in which this book is published, I am infinitely grateful to him.

In a previous publication, we tackled the transitions from digital to quantum communications in the context of engineering; as the quantum aspect was not discussed sufficiently, we will try to address this lacuna through this new work. In fact, it seems opportune to deepen our knowledge of quantum engineering via a work targeting practical aspects while still integrating the aspect of formalism and paying attention to clarity, comprehension and the concepts’ usefulness. This book therefore aims to address quantum communications and possible new applications in telecommunications. In collaboration with Professor Achour Benslama, who has been working on the question of the evolution of quantum mechanics, and Dr Aris Skander who has refined the laser and cryptography aspects, we will provide the scientific community with a work that aims for a synergy between the theoretical foundations of quantum communications and their current and future applications in the domain of telecommunications.

Malek BENSLAMAAchour BENSLAMANovember 2016

Introduction

The initial idea behind writing this work was to explore technological advances in quantum communications. The main inspiration was the famous quantum computer and all the technology that might lead to its creation. We could not avoid either the formalism of quantum mechanics, or the need to find concepts similar to signal processing to ensure its feasibility in practice. Nor could we evade the consequences of discussions between proponents of determinism (Einstein, Rosen and Podolsky) or those of randomness (Heisenberg and the Copenhagen School). Our preference for practicality prevailed over the more formal aspect. In reading the works of philosophers of science, we will in particular cite Michel Bitbol who supported the assertion that quantum mechanics is a generalized probability theory, in which we found some solace; we can therefore speak of processes, expected values, covariance, etc., and signal theory is not far off. Only the important aspects were worth including in our work: contextuality, non-locality, and specific inequalities that may be temporal, spatial or random. To do this, we have paid particular attention to Bell inequalities (for space), Kochen–Specker (for contextuality) or Leggett–Garg (for time), and the violation have also been noted due to the need for comprehensiveness. Two concepts specific to the quantum domain have also been addressed: decoherence and entanglement. Using explanatory diagrams, we have shown the benefits of these two concepts, and their consequences.

For more than 40 years all of our computers have functioned thanks to silicon electronics, which has enabled us to move from having 2,000 transistors on a chip in 1971 to more than six billion today. But 10 years from now, this frantic progression towards miniaturization risks reaching its limits, as dictated by the laws of physics. From 22 nm today, the etching of electronic chips is at risk of dropping to 16 nm in 2016 and finally 5 nm around 2020, which is the equivalent of almost 50 atoms side by side.

But to arrive at such a level of integration, electronics and IT will be confronted by two formidable barriers: one is technology and the other is economics. Scientists believe that it will be very difficult, in fact impossible, to drop below this limit of 5 nm without radically changing the technological approach; as a new arrival in this nano-world, electronics is dominated by the laws of quantum physics.

Moreover, many analyses emphasize that Moore’s law, which has governed developments in IT for almost half a century and predicts that the numbers of transistors on a single chip will double every 2 years, will also face the economic barrier of diminishing returns.

In concrete terms, when we have reached transistors of 10 nm, each reduction in the fineness of etching electronic circuits will demand greater and greater technological and industrial investments for an increase in speed and efficiency that is less and less perceptible to the consumer.

It is therefore absolutely necessary, for the reasons that have just been given, for IT to undergo major upheavals in the course of the next 10 years in order to prepare for the “after silicon” era, whose arrival is inexorably approaching.

Quantum communications can only be grasped through their essential element: the qubit and its derivatives (qudit, qutrit, ququad), as well underlying quantum circuitry. Quantum gates have therefore been postponed. Wigner distribution and the quantum Fourier transform have been developed.

The main applications for quantum communications in the domain of telecommunications are beginning to appear. For this, we will build on the developments achieved on quantum transistors, nanocrystals, and nanoclusters.

In optic fibers, we introduce the creation of light memories thanks to solitons, in which a laser beam circulates in a coiled electric fiber. In the near future, such lasers, threaded with optical solitons, may perhaps serve to store bits of information in looped fibers. The light will not only be a messenger: it will also be a memory. Thus, the recent marketing of the first LiFi (light fidelity) lamps, as well as terminals able to capture this new wireless technology using the LED light network (electroluminescent diodes) to transit and access data using the internet, will enable high-speed data transmission. This technology is faster than WiFi (wireless fidelity). Securing encrypted data and a specific location and ensuring its confidentiality, as only accessible in the light beam emitted by the LED, will be an important asset. Some other advantages generated by this technology can be summarized by the following points:

– no interference with radio transmission equipment;

– constant data transmission speed;

– absence of risks to health, no radio or electromagnetic transmission.

The importance of creating memories was one of our first reasons for introducing solitons.

In circuits, an evolution is now occurring in the transition from charge electronics to spin electronics. Most spin electronics nanosystems suffer from the same limitations as those of conventional electronics: they are sensitive to the dispersions of magnetic properties that become inevitable when we approach nanometric sizes and the limits of nano-structuring technologies. An original way of overcoming these problems linked to miniaturization is using magnetic nanometric configurations that enter the class of magnetic solitons. The solution could come from solitons. A characteristic property of a soliton is that its nature confers on it a great immunity to imperfections that defects in material and thermal fluctuations can create.

Another advantage is that magnetic solitons do not require an electrical supply to sustain themselves once created. Mastering their existence and manipulation has thus opened a new paradigm for the electronics of tomorrow, giving rise to new functionalities for pursuing miniaturization beyond the limits which are visible today. This, for us, constitutes a second reason for processing solitons. The development in solitons will be tackled via optic fibers.

Some elements of quantum technology have reached maturity and are available commercially, such as quantum key distribution systems. Other elements of quantum technology are now becoming realized, such as large-scale secure networks, quantum lithography and quantum IT processors. Photonics will occupy a central role in these technologies in regard to high-speed transmissions and weak photon properties. We therefore retain the fact that quantum photon technology will be one of the main sources of development in quantum communications. This has been proved by quantum entanglement, which has been tested experimentally by using photons generated from atom cascades. Non-linear processes for spontaneous parametric conversions have been a source of photon pairs for experiments in generating quantum states from a brilliant laser beam, and crushed states. Parametric conversion has also been used for quantum teleportation. One can also consider the interaction of single photons with single atoms in an optic cavity, which will be a major technology for photonic quantum technologies.

We will process photonics using crystals in a dedicated chapter (Chapter 6), which will highlight their use for routers and wave-length demultiplexers (WDM).

Devices with photonic band gap can be used to create WDMs. Light sources need to have a broad wavelength tunability, low chirping and great stability in temperature. These devices include ultra-selective filters, which are very useful for dense WDMs.

At the level of radiation, it is useful to think of photonic band gap antennae, as well as photonic antennae, which will be an integrating element in quantum communications technology.

Over recent decades, substantial theoretical and experimental progress has been made in understanding the quantum nature of physical phenomena, which is the basis of current and future technologies. Quantum correlations, such as the entanglement of composite system states and the phenomenon of quantum discord, which captures other aspects of quantum correlations, quantum contextuality and, linked to these phenomena, uncertainty relationships for conjugated variables and entropies, such as Shannon and Reyi entropies, and inequalities for spin states, such as Bell inequalities, reflect the quantum properties of micro- and macro-systems. The mathematical methods necessary for describing all the quantum phenomena mentioned above were the subject of intense study at the end of the last century, and at the beginning of this century.

The other new direction in elaborating the mathematical approach to quantum physics is tomography, which offers a new vision of quantum states. In the tomographic image of quantum mechanics, states are identified with equitable conditional probability distributions, which contain the same information on the states as the wave function of the matrix density. Mathematical methods for the tomographic approach are based on studying the star product (associative product) of the quantification scheme. The star tomographic product provides an additional understanding of the associated product, which is linked to the existence of specific pairs of operators called quantifiers and de-quantifiers [MAN 13].

Theoretically, it is important to remember key facts. In his article, Eli Maor specifies how he has been able to understand Heisenberg’s uncertainty principle [MAO 09]. Heisenberg’s uncertainty principle, feted as perhaps the most important principle of modern physics, was the most elusive of all. You cannot simultaneously determine a particle’s position and dynamic (i.e. speed) with absolute certainty. Any increase in the determinism of one of these quantities occurs to the detriment of the uncertainty principle of the others. This process immediately became one of the foundations of modern physics. Its influence on the way in which scientists think of the world has become very pervasive. It reaches beyond physics and has become part of our everyday language.

In quantum information theory, the non-communication theorem is a result that gives conditions in which the instantaneous transfer of information between two observers is impossible.

[ARA 11] gives a no-go theorem for probabilistically checkable proof (PCP), or probabilistic proof. Finally, to conclude this introduction, we come to consider the evolution of quantum mechanics above all for aspects dedicated to quantum communications [BLI 29].