Quantum information processing: from theory to experiment

372 Pages·2007·4.044 MB·English

by  Dimitris G. Angelakis, Matthias Christandl, Artur Ekert, Alastair Kay, Sergei Kulik

QUANTUM INFORMATION PROCESSING
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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
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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 impossi-
ble”. 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 cen-
tury 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 sci-
ence. 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
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