Quantum [Un]speakables Springer-Verlag Berlin Heidelberg GmbH ONLINE LIBRARY Physics and Astronomy http://www.springer.de/phys/ R.A. Bertlmann A. Zeilinger Quantum [Un]speakables From Bell to Quantum Information With 141 Figures, 4 in Color t Springer Professor Dr. Reinhold A. Bertlmann University of Vienna, Institute for Theoretical Physics Boltzmanngasse 5, 1090 Vienna, Austria e-mail: [email protected] Professor Dr. Anton Zeilinger University of Vienna, Institute for Experimental Physics Boltzmanngasse 5, 1090 Vienna, Austria e-mail: [email protected] Library of Congress Cataloging-in-Publication Data Quantum [un]speakables : from Bell to quantum information I [edited by] R.A. Bertimann, A. Zeilinger. p. cm. Includes biblographical references and index. ISBN 3540427562 (acid-free pa­ per) 1. Bell's theorem--Congresses. 3. Bell, J.S.--Congress. I. Bell, J.S. II. Bertlmann, Reinhold A. III. Zeilinger, Anton. QC174.17.B45 Q36 2002 530.12--dc21 2002021641 ISBN 978-3-642-07664-0 ISBN 978-3-662-05032-3 (eBook) DOI 10.1007/978-3-662-05032-2 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. http://www.springer.de © Springer-Verlag Berlin Heidelberg 2002 Originally published by Springer-Verlag Berlin Heidelberg N ew York in 2002 Softcover reprint of the hardcover 1St edition 2002 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant pro­ tective laws and regulations and therefore free for general use. Typesetting: Data conversion by LE-TEX Jelonek, Schmidt & Vockler GbR, Leipzig Cover design: design & production, Heidelberg Printed on acid-free paper SPIN: 10958216 56/3111 5 4 3 2 1 John Bell @Renate Bertlmann, 1980 Preface - From Bell to Quantum Information John Stewart Bell was certainly one of the really outstanding scientists of the Twentieth Century. The theorem named after him was most aptly called by Henry Stapp the most profound discovery since Copernicus. Born in Belfast in 1928, his scientific career up to his untimely death in 1990 covered not only the foundations of quantum mechanics, but also the areas of quantum field theory and the physics of accelerators, where he made outstanding contributions. So, the conference organized in his honor at the University of Vienna, 10-14 November 2000, to commemorate the Tenth Anniversary of his death brought together friends and colleagues working in all three areas. John Bell's scientific career began in Harwell and Malvern, where he made calculations of particle trajectories in accelerators and became an expert in high demand for the focusing of particle beams. During this time, he met his wife, Mary, who was also an accelerator physicist. We were very happy and grateful to have Mary Bell as the Guest of Honor at the Vienna Conference. Later, while working on his thesis with Rudolf Peierls at Birmingham, he discovered independently from G. Liiders and W. Pauli the CPT theorem, one of the most basic theorems in physics. This is probably the most fundamental symmetry principle which states that the joint action of charge conjugation, inversion of parity and time reversal leaves any physical system unchanged. Of his contributions to quantum field theory, two others could be men­ tioned. One is the discovery, together with Roman Jackiw, of what is to­ day called the Bell-Jackiw-Adler anomaly. It explains some hitherto-not­ understood pion decays by adding divergences of the quantum current to the description of the system. The other most important contribution of John Bell is his suggestion in 1967 that there should exist a gauge theory describing weak interactions. This idea had an immense influence on Martinus Veltman and Gerard 't Hooft and resulted in a full understanding of the weak force. Ultimately, gauge theories became the standard tool of modern particle physics. While it is difficult to underestimate the importance of John Bell's contri­ butions to accelerator physics and to field theory, his most important contri­ butions were certainly in the foundations of quantum mechanics. Evidently, John Bell had been interested from a very early stage in the philosophical VIII Preface issues raised by quantum theory, a topic not very popular during his student days at Queen's University, Belfast. Apparently, John Bell, who had been interested in the Bohr-Einstein dialogue, always took the position of Albert Einstein on philosophical issues. He also felt that a completion of quantum mechanics using so-called "hidden variables" would be highly desired, as it would help to regain a realistic and objective picture of the world. That way, Bell hoped one would be able to arrive at a physics where "measurement" would not play such a central role as in the Copenhagen interpretation of quantum mechanics. Then, a most interesting sequence of events set in. In 1952, David Bohm had achieved something which had earlier been proclaimed impossible. It had been proved by John von Neumann that no hidden variable theory could agree with quantum mechanics. Bohm actually formulated such a theory, where each particle at any time has both a well-defined position and a well­ defined momentum. The conflict raised between von Neumann and Bohm was elegantly resolved by Bell, who showed that von Neumann's proof contained a physically unjustifiable assumption. So while John Bell had flung open the door widely for hidden variable theories, he immediately dealt them a major blow. In 1964, in his celebrated paper "On the Einstein-Podolsky-Rosen Paradox", he showed that any hidden variable theory, which obeys Einstein's requirement of locality, i.e. no influence travelling faster than the speed of light, would automatically be in conflict with quantum mechanics. This is the celebrated Bell's theorem, which even found entrance into comics. Surprisingly, while quantum mechanics was already well established at the time of the publication of Bell's theorem, no experiments existed which definitely allowed one to rule out a local realistic interpretation. Which means that no experiment had measured for those specific two-particle correlations which are so necessary to demonstrate the violation of Bell's inequality, the quantitative measure of the border of the validity of local realism. Since then, experimentation has become better and better, and by now an impressive body of evidence has been collected, supporting quantum mechanics and being in conflict with local realism. While a very tiny loophole in principle remains for local realism, it is a very safe position to assume that quantum mechanics has definitely been shown to be the right theory. Thus, a very deep philosophical question, namely, whether or not events observed in the quantum world can be described by an underlying deterministic theory, has been answered by experiment, thanks to the momentous achievement of John Bell. This achievement is even more remarkable as he was able to rule out a gigantic class of theories, without having to know any details of the theories. Today, experimental development has gone far beyond this. Bell's in­ equality and the underlying physics of entangled states have become cor­ nerstones of the newly evolving technology of quantum information. There, information is encoded, transmitted and processed in completely novel ways Preface IX based on quantum laws. A bit of information can be encoded in a quantum superposition. Two quantum bits or q-bits can be entangled over long dis­ tances, and entanglement can be used to encode information in a novel way unprecedented in classical physics. Experimentally, it has been shown that, using entanglement, one can encode more information than one bit in a two­ state system, one can teleport a quantum state over large distances and one can use quantum entanglement to provide a cryptographic method which is secure against eavesdropping by the laws of physics and not by a trick of the experimentalist. Finally, quantum computation promises exponential speed­ up for certain problems, and first steps have been taken in the direction of quantum computation in various laboratories all over the world. It is most interesting to note that, despite his own theorem, John Bell continued to be an advocate of realistic hidden variable theories, which now, according to his own findings, have to be non-local. Therefore, he became an advocate of theories proposed by Ghirardi, Rimini, Weber, Peierls and Gisin, theories that, no matter how little, deviate from quantum mechanics and thus might be ruled out by experiment someday. Thus, even if John Bell in the end might not have turned out to be on the right side when it comes to the fundamentals of the interpretation of quantum mechanics, this should never be held against him. In contrast, he was one of the few, like Albert Einstein, who realized how extremely strange the consequences of quantum mechanics, if it finally should turn out to be the ultimate correct theory, are for our view of the world, and it is a sign of his high moral distinction that he was not at all willing to give in easily. In conclusion, it might very well turn out in the future that Bell's theorem paved the way to a momentous change of our conception of the world.