Table Of ContentThe New Quantum Age
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The New Quantum Age
From Bell’s Theorem to
Quantu(cid:2)m Computation
and Teleportation
Andrew Whitaker
Department of Physics
Queen’s University Belfast
1
3
Great Clarendon Street, Oxford ox2 6dp
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© Andrew Whitaker 2012
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First published 2012
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For John and Peter
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Preface
Over the past half-century, the approach of the community of physicists
to quantum theory has changed quite markedly. At the beginning of the
1960s, the theory was regarded as a superlative tool for the study of
physical systems—atoms, molecules, nuclei, radiation, and those prop-
erties of solids where their atomic nature was central to the behaviour.
However, it was considered totally inappropriate even to think with any
novelty about the fundamental nature of quantum theory and its rather
surprising properties. That, it was practically universally believed, had
been sorted out once and for all by Niels Bohr thirty years before.
Fifty years or so later, it has been fairly generally realized that Bohr’s
ideas were not necessarily the fi nal word on the topic, that the theory
itself certainly merited and still merits much further analysis, and that
the theory may inform us, not just of the behaviour of physical systems,
but also of fundamental and important aspects of the Universe itself.
Also, and perhaps even more surprisingly, this deeper analysis of the
theory has led to the development of the new topic of study of quantum
information theory, which may revolutionize several aspects of com-
munication and computation.
This book describes the changes that have taken place, and discusses
some of the new ideas current in both quantum theory and quantum
information theory. I have also taken the opportunity to give an account
of some of those scientists mostly responsible for the change in attitude
over this period. I hope that the book will be accessible to anybody
interested in the topic; to paraphrase Einstein, it might be said that
I have tried to make things as simple as possible, but no simpler, given
that I do not wish to avoid even some of the more complex aspects of
the topic.
I should state that the initial idea of the book was that it should be
written jointly by Dipankar Home and myself. However, after initial
planning, Dipankar had unfortunately to drop out because of other com-
mitments. I acknowledge his contribution to the planning of the book.
I would also particularly thank Reinhold Bertlmann and Anton
Zeilinger for a particular contribution to this book. About ten years ago
I was privileged to speak at Q uantum [Un]Speakables , a conference
they organized in Vienna to celebrate the work of John Bell and his
viii Preface
followers. Among those attending this conference were virtually all
those who contributed to the rise of the study of quantum foundations,
and the early days of quantum information theory. Renate Bertlmann
took a unique set of photographs of the participants, and I would thank
Renate, Reinhold, and Anton for permission to use many of these in
this book. I would also like to thank Gerlinde Fritz who arranged for
me to receive these pictures. In the caption they are referred to as
[ © Zentralbibliothek für Physik, Renate Bertlmann].
I would also like to thank Queen’s University Belfast for my appoint-
ments as Emeritus Professor and Visiting Senior Research Fellow that
have enabled me to complete this book.
At Queen’s, I would like to thank Joan Whitaker, Subject Librarian
in Mathematics and Physics, for considerable help in tracing books,
papers, and pictures.
I would also thank all the publishers and authors who have given
permission for the reproduction in this book of copyright fi gures and
pictures. Every effort has been made to contact the holders of copyright
in materials reproduced in this book. I apologize for any omissions,
which will be rectifi ed in future printings if notice is given to the
publisher.
At Oxford University Press, I would thank Sonke Adlung, April
Warman, and Clare Charles for their courtesy and helpfulness in various
aspects of the writing of this book. I would also like to thank Charles
Lauder Jr for highly effi cient and helpful copyediting, and Marionne
Cronin, Emma Lonie, and Vijayasankar Natesan at Oxford University
Press and SPi for all their hard work in the production of this volume.
Lastly I would thank my wife, Joan, and children, John and Peter,
for their support and tolerance while I have been writing the book.
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Contents
Introduction: The First Quantum Age and
the New Quantum Age 1
Part I The First Quantum Age 3
1 Quantum theory—basic ideas 5
albert einstein 8
2 Quantum theory and discreteness 11
max planck 12
3 The Schrödinger equation 19
The time-independent Schrödinger equation,
eigenfunctions, and eigenvalues 19
erwin schrödinger 20
niels bohr 22
The time-dependent Schrödinger equation
and wave-functions 24
4 Superposition 27
Superposition 27
The Born probability rule or interpretation 28
max born 29
The conceptual challenges posed by superposition 31
The measurement problem of quantum theory 33
john von neumann 34
Hidden variables 36
louis de broglie 38
wolfgang pauli 39
5 Further complications 41
Measurement of other observables 41
Wave and particle, and the Heisenberg principle 44
werner heisenberg 45
pascual jordan 46
paul dirac 47
States of a spin- –1 particle; photon polarization states 50
2
