Table of contents for Introduction to quantum information science / Vlatko Vedral.


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PART I CLASSICAL AND QUANTUM INFORMATION
SClassical information                                                3
.1i Information and physics                                         3
L.2  Quantifying information                                        4
1.3  Data compression                                               7
1.4  Related measures of information                                8
P4A.1 Relative entropy                                          9
1.4.2 Joint entropy                                            10
1.4.3 Conditional entropy                                      10
.4.4 Mutual information                                        10
1L5  Capacity of a noisy channel                                   11
1P6  Summary                                                       12
2   Quantum mechanics                                                  14
2,1  Dirac notation                                                14
122  The qubit, higher dimensions, and the inner product           16
2.3  Hilbert spaces                                                17
2.4  Projective measurements and operations                        19
.5  Unitary operations                                             20
16   Eingenvectors and eigenvalues                                 21
2.   Spectral decomposition                                        22
2.8  Applications of the spectral theorem                          23
2.9  Dirac notation shorthands                                     24
2.10 The Mach-Zehnder interferometer                               25
2.11 The postulates of quantum mechanics                           27
2. 2 Mixed states                                                  28
2.13 Entanglement                                                  29
2.14 Summary                                                       30
3  Quantum information--the basics                                     31
3. i No cloning of quantum bits                                    31
3.2  Quaatum cryptography                                          33
3.3  The trace and partial-trace operations                        35
3.4  Hilbert space extension                                       37
35   The Schmidt decomposition                                     38
3.6  Generalized measurements                                      40
3.7  CP-maps and positive operator-valued measurements             41
3.8  The postulates of quantum mechanics revisited                 42
3.9  Summary    .42
4   Quantum communication with entanglement                           44
4.   Pure state entanglement and Pauli matrices                    44
4.2  Dense coding                                                  45
4.3  Teleportation                                                 46
4,4  Entanglement swapping                                         48
4,5  No instantaneous transfer of information                      19
4.6  The extended-Hilbert-space view                               50
4.7  Summary                                                       50
5   Quantum information I                                             52
5.1  Fidelity                                                      53
5,2  Helstror's discrimination                                     54
5.3  Quantum data compression                                      55
5,4  Entropy of observation                                        58
5,5  Conditional entropy and mutual information                    59
5.6  Relative entropy                                              61
5.7  Statistical interpretation of relative entropy                62
5.8  Summary                                                       66
6   Quantum information II                                            68
6.1  Equalities and inequalities related to entropy                68
6.2  The Holevo bound                                              71
6.3  Capacity of a bosonic channel                                 73
6.4 Information gained through measurements                        75
6.5  Relative entropy and thermodynamics                           76
6.6  Entropy increase due to erasure                               77
6.7  Landauer's erasure and data compression                       78
6.8  Summary                                                       78
PART II QUANTUM ENTANGLEMENT
7  Quantum entanglement-introduction                                  8i
7.1  The historical background of entanglement                     81
7.2  Bell's inqualities                                            83
7.3  Separable states                                              85
7.4  Pure states and Bel's inequalities                            86
7.5  Mixed states and Bell's inequalities                          87
7.6  Entanglement in second quantization                           87
7.7  Summary                                                       91
8  Witnessing quantum entanglement                                    92
8.1  Entanglement witnesses                                        93
8.2  The Jamiolkowski isomorphism                                  95
8.3  The Peres-Horodecki criterion                                  97
8.4  More examples of entanglement witnesses                        99
8.5  Summary                                                       100
9   Quantum entanglement in practice                                   102
9.1  Measurements with a Mach-Zehnder interferometer               102
9.2 Interferometric implementation of Peres-Horodecki criterion    104
9.21  Measuring tr 92?                                       104
9.2.2 Generalization to tr k                                  105
9,2.3 Measuring tr (p') "I                                    106
93   Measuring the fidelity between g and c(                       106
9.4  Summary                                                       107
10 Measures of entanglement                                            108
10.1 Distillation of multiple copies of a pure state               108
10.2 Analogy with the Carnot Cycle                                 110
10.3 Properties of entanglement measures                           111
10.4 Entanglement of pure states                                   113
10i5 Entanglement of mixed states                                  113
10.6 Measures of entanglement derived from relative entropy        117
10 7 Classical information and entanglement                        121
10.8 Entanglement and thermodynamics                               123
10.9 Summary                                                       128
PARiT II QUANTUM COMPUTATION
"11 Quantum algorithms                                                131
11.1 Coumputational complexity                                     131
S1. 2 Deutsch's atgorithm                                          133
11.2.1 Deutsch's algorithm and the Holevo bound               135
11.3 Oracles                                                       136
.14 Grover's search algorithm                                     137
11.5 Quantum factorization                                         140
11.5.1 Factorization                                          141
11..2 The quantum Fourier transform                           142
11.5.3 Phase estimation                                       144
11.6 Summary                                                       145
12 Entanglement, computation and quantum measurements                 146
12.01 Optimization of searches using entanglement                 147
12.2 Model for quantum measurement                                 149
12.3 Correlations and quantum measurement                          151
12.4 The ultimate limits of computation: the Bekenstein bound      157
12.5 Summary                                                       158
Q3 Quantum error correction                                           160
13.1 Introduction                                                  160
13.2 A simple example                                              160
133 General conditions                                             162
13.4 Reliable quantum computation                                   165
13.5 Quantum error correction considered as a Maxwell's demon      167
13.5.1 Pure states                                             171
13.5.2 Mixed states                                            172
13.6 Summary                                                       173
14 Outlook                                                             175



Library of Congress subject headings for this publication: Quantum theory, Quantum communication