Introduction to Quantum Information Science

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Format: Hardcover
Pub. Date: 2007-04-05
Publisher(s): Oxford University Press
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Summary

This book offers a concise and up-to-date introduction to the popular field of quantum information. It has originated in a series of invited lecture courses at various universities in different countries. This is reflected in its informal style of exposition and presentation of key results inthe subject. In addition to treating quantum communication, entanglement and algorithms in great depth, this book also addresses a number of interesting miscellaneous topics, such as Maxwell's demon, Landauer's erasure, the Bekenstein bound and Caratheodory's treatment of the Second law ofthermodyanmics. All mathematical derivations are based on clear physical pictures which make even the most involved results - such as the Holevo bound - look comprehensible and transparent. The book is ideal as a first introduction to the subject, but may also appeal to the specialist due to itsunique presentation.

Author Biography


Vlatko Vedral
Centenary Professor of Quantum Information
School of Physics and Astronomy
University of Leeds
Leeds LS2 9JT
Vlatko Vedral studied his undergraduate degree and PhD at Imperial College (1992-1998). After graduating from his PhD in 1998, he took up a junior research fellowship at Merton College in Oxford where he stayed for two years (1998-2000). He returned to Imperial College in 2000 as a governors' lecturer and was promoted to reader in 2003. In October 2004 he moved to Leeds University as the centenary professor of Quantum Information Science. He has taught at many different universities and held visiting professorships at Oxford, Vienna, Singapore and Perimeter Institute in Canada.
Vlatko Vedral is an active researcher in quantum information and quantum mechanics, having published over 100 papers in these fields. He enjoys explaining science to the media and has been interviewed on a number of occasions regarding his work and the state of the field. He has contributed to several introductory books on quantum computing as well as written a textbook on Quantum Optics.

Table of Contents

Classical and 3d Quantum Information
Classical informationp. 3
Information and physicsp. 3
Quantifying informationp. 4
Data compressionp. 7
Related measures of informationp. 8
Relative entropyp. 9
Joint entropyp. 10
Conditional entropyp. 10
Mutual informationp. 10
Capacity of a noisy channelp. 11
Summaryp. 12
Quantum mechanicsp. 14
Dirac notationp. 14
The qubit, higher dimensions, and the inner productp. 16
Hilbert spacesp. 17
Projective measurements and operationsp. 19
Unitary operationsp. 20
Eigenvectors and eigenvaluesp. 21
Spectral decompositionp. 22
Applications of the spectral theoremp. 23
Dirac notation shorthandsp. 24
The Mach-Zehnder interferometerp. 25
The postulates of quantum mechanicsp. 27
Mixed statesp. 28
Entanglementp. 29
Summaryp. 30
Quantum information-the basicsp. 31
No cloning of quantum bitsp. 31
Quantum cryptographyp. 33
The trace and partial-trace operationsp. 35
Hilbert space extensionp. 37
The Schmidt decompositionp. 38
Generalized measurementsp. 40
CP-maps and positive operator-valued measurementsp. 41
The postulates of quantum mechanics revisitedp. 42
Summaryp. 42
Quantum communication with entanglementp. 44
Pure state entanglement and Pauli matricesp. 44
Dense codingp. 45
Teleportationp. 46
Entanglement swappingp. 48
No instantaneous transfer of informationp. 49
The extended-Hilbert-space viewp. 50
Summaryp. 50
Quantum information Ip. 52
Fidelityp. 53
Helstrom's discriminationp. 54
Quantum data compressionp. 55
Entropy of observationp. 58
Conditional entropy and mutual informationp. 59
Relative entropyp. 61
Statistical interpretation of relative entropyp. 62
Summaryp. 66
Quantum information IIp. 68
Equalities and inequalities related to entropyp. 68
The Holevo boundp. 71
Capacity of a bosonic channelp. 73
Information gained through measurementsp. 75
Relative entropy and thermodynamicsp. 76
Entropy increase due to erasurep. 77
Landauer's erasure and data compressionp. 78
Summaryp. 78
Quantum Entanglement
Quantum entanglement-introductionp. 81
The historical background of entanglementp. 81
Bell's inequalitiesp. 83
Separable statesp. 85
Pure states and Bell's inequalitiesp. 86
Mixed states and Bell's inequalitiesp. 87
Entanglement in second quantizationp. 87
Summaryp. 91
Witnessing quantum entanglementp. 92
Entanglement witnessesp. 93
The Jamiolkowski isomorphismp. 95
The Peres-Horodecki criterionp. 97
More examples of entanglement witnessesp. 99
Summaryp. 100
Quantum entanglement in practicep. 102
Measurements with a Mach-Zehnder interferometerp. 102
Interferometric implementation of Peres-Horodecki criterionp. 104
Measuring tr <$$$>2?p. 104
Generalization to tr <$$$>kp. 105
Measuring tr (<$$$>T2)kp. 106
Measuring the fidelity between <$$$> and ¿p. 106
Summaryp. 107
Measures of entanglementp. 108
Distillation of multiple copies of a pure statep. 108
Analogy with the Carnot Cyclep. 110
Properties of entanglement measuresp. 111
Entanglement of pure statesp. 113
Entanglement of mixed statesp. 113
Measures of entanglement derived from relative entropyp. 117
Classical information and entanglementp. 121
Entanglement and thermodynamicsp. 123
Summaryp. 128
Quantum Computation
Quantum algorithmsp. 131
Computational complexityp. 131
Deutsch's algorithmp. 133
Deutsch's algorithm and the Holevo boundp. 135
Oraclesp. 136
Grover's search algorithmp. 137
Quantum factorizationp. 140
Factorizationp. 141
The quantum Fourier transformp. 142
Phase estimationp. 144
Summaryp. 145
Entanglement, computation and quantum measurementsp. 146
Optimization of searches using entanglementp. 147
Model for quantum measurementp. 149
Correlations and quantum measurementp. 151
The ultimate limits of computation: the Bekenstein boundp. 157
Summaryp. 158
Quantum error correctionp. 160
Introductionp. 160
A simple examplep. 160
General conditionsp. 162
Reliable quantum cumputationp. 165
Quantum error correction considered as a Maxwell's demonp. 167
Pure statesp. 171
Mixed statesp. 172
Summaryp. 173
Outlookp. 175
Bibliographyp. 179
Indexp. 181
Table of Contents provided by Ingram. All Rights Reserved.

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