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QUANTUM INFORMATION PROCESSING NATO Science Series A series presenting the results of scientific meetings supported under the NATO Science Programme. The series is published by IOS Press and Springer Science and Business Media in conjunction with the NATO Public Diplomacy Division. Sub-Series I. Life and Behavioural Sciences IOS Press II. Mathematics, Physics and Chemistry Springer Science and Business Media III. Computer and Systems Sciences IOS Press IV. Earth and Environmental Sciences Springer Science and Business Media V. Science and Technology Policy IOS Press The NATO Science Series continues the series of books published formerly as the NATO ASI Series. The NATO Science Programme offers support for collaboration in civil science between scientists of countries of the Euro-Atlantic Partnership Council. The types of scientific meeting generally supported are “Advanced Study Institutes” and “Advanced Research Workshops”, although other types of meeting are supported from time to time. The NATO Science Series collects together the results of these meetings. The meetings are co-organized by scientists from NATO countries and scientists from NATO’s Partner countries – countries of the CIS and Central and Eastern Europe. Advanced Study Institutes are high-level tutorial courses offering in-depth study of latest advances in a field. Advanced Research Workshops are expert meetings aimed at critical assessment of a field, and identification of directions for future action. As a consequence of the restructuring of the NATO Science Programme in 1999, the NATO Science Series has been re-organized and there are currently five sub-series as noted above. Please consult the following web sites for information on previous volumes published in the series, as well as details of earlier sub-series: http://www.nato.int/science http://www.springeronline.nl http://www.iospress.nl http://www.wtv-books.de/nato_pco.htm Series III: Computer and Systems Sciences – Vol. 199 ISSN: 1387-6694 Quantum Information Processing From Theory to Experiment Edited by Dimitris G. Angelakis University of Cambridge, United Kingdom Matthias Christandl University of Cambridge, United Kingdom Artur Ekert University of Cambridge, United Kingdom and National University of Singapore Alastair Kay University of Cambridge, United Kingdom and Sergei Kulik Moscow M.V. Lomonosov State University, Russia Amsterdam • Berlin • Oxford • Tokyo • Washington, DC Published in cooperation with NATO Public Diplomacy Division Proceedings of the NATO Advanced Study Institute on Quantum Computation and Quantum Information Chania, Crete, Greece 2–13 May 2005 © 2006 IOS Press. All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without prior written permission from the publisher. ISBN 1-58603-611-4 Library of Congress Control Number: 2006927263 Publisher IOS Press Nieuwe Hemweg 6B 1013 BG Amsterdam Netherlands fax: +31 20 687 0019 e-mail: [email protected] Distributor in the UK and Ireland Distributor in the USA and Canada Gazelle Books Services Ltd. IOS Press, Inc. White Cross Mills 4502 Rachael Manor Drive Hightown Fairfax, VA 22032 Lancaster LA1 4XS USA United Kingdom fax: +1 703 323 3668 fax: +44 1524 63232 e-mail: [email protected] e-mail: [email protected] LEGAL NOTICE The publisher is not responsible for the use which might be made of the following information. PRINTED IN THE NETHERLANDS Quantum Information Processing v D.G. Angelakis et al. (Eds.) IOS Press, 2006 © 2006 IOS Press. All rights reserved. Introduction By Artur EKERT Chania, a picturesque little town on the coast of the western Crete, the birthplace of Dimitris Angelakis, the main organizer of this Advanced Study Institute in Quantum Information Sci- ence, is only a few miles away from the tiny island of Antikythera. In 1900 a party of sponge-divers were driven by a storm to anchor near the island and there, at a depth of some 40 meters, they found the wreck of an ancient cargo ship. Among the pieces of pottery and marble statutes sprawled on the seabed was a coral-encrusted lump of corroded bronze gear wheels. The Antikythera mechanism, as it is now known, was probably the world’s first “analog computer” — a sophisticated device for calculating the motions of stars and planets. This remarkable assembly of more than 30 gears with a differential mechanism, made on Rhodes or Cos in the first century B.C., revised the view of what the ancient Greeks were capable of creating at that time. A comparable level of engineering didn’t become widespread until the industrial revo- lution nearly two millennia later. Thus it is hardly surprising that Richard Feynman, who saw the Antikythera mechanism on display in Athens, called it “nearly impossible”. In one of his letters, reprinted in “What Do You Care What Other People Think?: Further Adventures of a Curious Character”, he wrote “… Yesterday morning I went to the archaeological museum. … Also, it was slightly boring because we have seen so much of that stuff before. Except for one thing: among all those art objects there was one thing so entirely different and strange that it is nearly impossible. It was recovered from the sea in 1900 and is some kind of ma- chine with gear trains, very much like the inside of a modern wind-up alarm clock. The teeth are very regular and many wheels are fitted closely together…” It seems likely that the Antikythera tradition of complex mechanical technology was transmitted via the Arab world to medieval Europe where it formed the basis of clockmaking techniques. As such, the Antikythera mechanism is a venerable precursor of mechanical computing devices based on the meshing of metal gears. Indeed, for many years the basic raw material of the computer industry was brass. The 17th century calculators of Wilhelm Schickard, Blaise Pascal and Gottfried Wilhelm Leibniz testify to the importance of gears in the history of computing. When, in 1837, Charles Babbage was tinkering with a design of the first programmable computer, known as the Analytical Engine, he was thinking in terms of rods, gears and wheels. vi From gears to relays to valves to transistors to integrated circuits and so on – in the 20th century brass gave way to silicon. Today’s advanced lithographic techniques can etch logic gates and wires less than a micron across onto the surfaces of silicon chips. Soon they will yield even smaller components, until we reach the point where logic gates are so small that they consist of only a few atoms each. If computers are to con- tinue to become faster (and therefore smaller), new, quantum technology must replace or supplement what we have now, but it turns out that such technology can offer much more than smaller and faster microprocessors. It can support entirely new modes of computation, with new quantum algorithms that do not have classical analogues. The very same person who was so fascinated by the ancient Antikythera laid down the foundations of quantum computation. In 1981 Feynman observed that simulations of some quantum experiments on any classical computer appear to involve an exponen- tial slowdown in time as compared to the natural run of the experiment. Instead of viewing this fact as an obstacle, Feynman regarded it as an opportunity. If it requires so much computation to work out what will happen in a complicated quantum experiment then, he argued, the very act of setting up an experiment and measuring the outcome is tantamount to performing a complex computation. After all, any real computation is a physical process, be it classical or quantum. Thus any computation can be viewed in terms of physical experiments which produce outputs that depend on initial prepara- tions called inputs. Since then, the hunt has been on for interesting things for quantum computers to do, and at the same time, for the scientific and technological advances that could allow us to build quantum computers. The NATO Advanced Study Institute in Chania brought together a number of re- searchers and students in both experimental and theoretical quantum information science. During lectures and talks, and in numerous discussions over Raki, the participants shared their views on just about everything; from quantum algorithms and intricacies of computational complexity to the finer parts of Cretan cuisine, and from new technolo- gies for realizing quantum computers to the spirit of traditional Greek dances. The knowledge that nature can be coherently controlled and manipulated at the quantum level was perceived as both a powerful stimulus and one of the greatest challenges fac- ing experimental physics. Fortunately the exploration of quantum technology has many staging posts along the way, each of which will yield scientifically and technologically useful results and some of them are described in this volume. We hope this collection of papers provides a good overview of the current state-of- the-art of quantum information science. We do not know how a quantum Antikythera will look like but all we know is that the best way to predict the future is to create it. From the perspective of the future, it may well be that the real computer age has not yet even begun. We also wish to thank our sponsors NATO, the Cambridge-MIT Institute, the Un- ion of Agricultural Cooperatives of Kidonia and Kissamos, the Cooperative Bank of Chania, ANEK Lines, Olympic Airways, ABEA Olive Oil Products and Stigmes Magazine. Finally we acknowledge the helpful collaboration from IOS Press in the publication of this volume and also thank Kaija Hampson for being an excellent secre- tary during the meeting. vii Contents Introduction v Artur Ekert Chapter 1. Quantum Communication and Entanglement Quantum Entanglement: Detection Methods and Usefulness as a Physical Resource 3 Dagmar Bruß On Quantum Cryptography with Bipartite Bound Entangled States 19 Paweł Horodecki and Remigiusz Augusiak Unitary Local Permutations on Bell Diagonal States of Qudits and Quantum Distillation Protocols 30 Hector Bombin and Miguel A. Martin-Delgado Quantum Communication Channels in Infinite Dimensions 41 Alexander S. Holevo Introduction to Relativistic Quantum Information 61 Daniel Terno Generalized Bell Inequalities and the Entanglement of Pure States 83 Kwek Leong-Chuan, Chunfeng Wu, Jingling Chen, Dagomir Kaszlikowski and C.H. Oh Thermal Entanglement in Infinite Dimensional Systems 89 Aires Ferreira, Ariel Guerreiro and Vlatko Vedral Improved Algorithm for Quantum Separability and Entanglement Detection 93 Lawrence M. Ioannou, Benjamin C. Travaglione, Donny Cheung and Artur K. Ekert Generalised Entanglement Swapping 99 Anthony J. Short, Sandu Popescu and Nicolas Gisin Quantum Information Processing with Low-Dimensional Systems 103 Alexander Yu. Vlasov Local Information and Nonorthogonal States 109 Jonathan Walgate Optimal Alphabets for Noise-Resistant Quantum Cryptography 113 Denis Sych, Boris Grishanin and Victor Zadkov Chapter 2. Quantum Algorithms and Error Correction Quantum Algorithms and Complexity 121 Michele Mosca viii An Introduction to Measurement Based Quantum Computation 137 Richard Jozsa Quantum Error Correction and Fault-Tolerance 159 Daniel Gottesman Simulating Fourier Transforms for Open Quantum Systems in Higher Encoding Bases 170 Ioannis N. Doxaras Entanglement, Area Law and Group Theory 175 Radu Ionicioiu, Alioscia Hamma and Paolo Zanardi A Quantum Algorithm for Closest Pattern Matching 180 Paulo Mateus and Yasser Omar Classical and Quantum Fingerprinting in the One-Way Communication Model 184 Anthony J. Scott, Jonathan Walgate and Barry C. Sanders Chapter 3. Quantum Information Theory in Spin Systems Introduction to Localizable Entanglement 191 Markus Popp, Frank Verstraete, Miguel A. Martin-Delgado and Ignacio Cirac State Transfer in Permanently Coupled Quantum Chains 218 Daniel Burgarth, Vittorio Giovannetti and Sougato Bose Geometric Effects in Spin Chains 238 Marie Ericsson and Alastair Kay Quantum Walks and Decoherence on a 1+1 Lattice 242 Isabelle Herbauts Certain Aspects of Quantum Random Walk Asymptotics 246 Ioannis Smyrnakis Chapter 4. Implementations of Quantum Information Processing From Entanglement to Quantum Key Distribution 255 Hannes Hübel and Anton Zeilinger Preparation and Measurement of Qutrits Based on Single-Mode Biphotons 281 Sergei Kulik Cavity Quantum Electrodynamics: Quantum Entanglement and Information 294 Jean-Michel Raimond Possibility of Quantum Computation by Utilizing Carbon Nanotubes – Cooper Pair Splitting by Tomonaga-Luttinger Liquid – 312 Junji Haruyama, K. Murakami, J. Mizubayashi and N. Kobayashi Implementing Quantum Processors in the Solid State 321 Crispin H.W. Barnes ix Quantum Field Trajectories Under Photon Number QND Measurement 326 Alexander A. Bukach and Sergei Ya. Kilin Quantum Computation Beyond the “Standard Circuit Model” 330 Konstantinos Ch. Chatzisavvas, Costas Daskaloyannis and Christos P. Panos Entangled Light from Optical Time Boundaries 337 Ariel Guerreiro, Aires Ferreira, José T. Mendonça and Vlatko Vedral Strong Light-Matter Coupling: Parametric Interactions in a Cavity and Free-Space 341 Igor B. Mekhov, Valentin S. Egorov, Victor N. Lebedev, Peter V. Moroshkin, Igor A. Chekhonin and Sergei N. Bagayev Macroscopic Quantum Information Channel Via the Polarization-Sensitive Interaction Between the Light and Spin Subsystems 346 Oksana S. Mishina, Dmitriy V. Kupriyanov and Eugene S. Polzik From Network Complexity to Time Complexity Via Optimal Control 353 Thomas Schulte-Herbrüggen, Andreas Spörl, Navin Khaneja and Steffen Glaser Author Index 359 This page intentionally left blank