
Introduction to Quantum Information Science
by Vedral, Vlatko-
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Summary
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 information | p. 3 |
Information and physics | p. 3 |
Quantifying information | p. 4 |
Data compression | p. 7 |
Related measures of information | p. 8 |
Relative entropy | p. 9 |
Joint entropy | p. 10 |
Conditional entropy | p. 10 |
Mutual information | p. 10 |
Capacity of a noisy channel | p. 11 |
Summary | p. 12 |
Quantum mechanics | p. 14 |
Dirac notation | p. 14 |
The qubit, higher dimensions, and the inner product | p. 16 |
Hilbert spaces | p. 17 |
Projective measurements and operations | p. 19 |
Unitary operations | p. 20 |
Eigenvectors and eigenvalues | p. 21 |
Spectral decomposition | p. 22 |
Applications of the spectral theorem | p. 23 |
Dirac notation shorthands | p. 24 |
The Mach-Zehnder interferometer | p. 25 |
The postulates of quantum mechanics | p. 27 |
Mixed states | p. 28 |
Entanglement | p. 29 |
Summary | p. 30 |
Quantum information-the basics | p. 31 |
No cloning of quantum bits | p. 31 |
Quantum cryptography | p. 33 |
The trace and partial-trace operations | p. 35 |
Hilbert space extension | p. 37 |
The Schmidt decomposition | p. 38 |
Generalized measurements | p. 40 |
CP-maps and positive operator-valued measurements | p. 41 |
The postulates of quantum mechanics revisited | p. 42 |
Summary | p. 42 |
Quantum communication with entanglement | p. 44 |
Pure state entanglement and Pauli matrices | p. 44 |
Dense coding | p. 45 |
Teleportation | p. 46 |
Entanglement swapping | p. 48 |
No instantaneous transfer of information | p. 49 |
The extended-Hilbert-space view | p. 50 |
Summary | p. 50 |
Quantum information I | p. 52 |
Fidelity | p. 53 |
Helstrom's discrimination | p. 54 |
Quantum data compression | p. 55 |
Entropy of observation | p. 58 |
Conditional entropy and mutual information | p. 59 |
Relative entropy | p. 61 |
Statistical interpretation of relative entropy | p. 62 |
Summary | p. 66 |
Quantum information II | p. 68 |
Equalities and inequalities related to entropy | p. 68 |
The Holevo bound | p. 71 |
Capacity of a bosonic channel | p. 73 |
Information gained through measurements | p. 75 |
Relative entropy and thermodynamics | p. 76 |
Entropy increase due to erasure | p. 77 |
Landauer's erasure and data compression | p. 78 |
Summary | p. 78 |
Quantum Entanglement | |
Quantum entanglement-introduction | p. 81 |
The historical background of entanglement | p. 81 |
Bell's inequalities | p. 83 |
Separable states | p. 85 |
Pure states and Bell's inequalities | p. 86 |
Mixed states and Bell's inequalities | p. 87 |
Entanglement in second quantization | p. 87 |
Summary | p. 91 |
Witnessing quantum entanglement | p. 92 |
Entanglement witnesses | p. 93 |
The Jamiolkowski isomorphism | p. 95 |
The Peres-Horodecki criterion | p. 97 |
More examples of entanglement witnesses | p. 99 |
Summary | p. 100 |
Quantum entanglement in practice | p. 102 |
Measurements with a Mach-Zehnder interferometer | p. 102 |
Interferometric implementation of Peres-Horodecki criterion | p. 104 |
Measuring tr <$$$>2? | p. 104 |
Generalization to tr <$$$>k | p. 105 |
Measuring tr (<$$$>T2)k | p. 106 |
Measuring the fidelity between <$$$> and ¿ | p. 106 |
Summary | p. 107 |
Measures of entanglement | p. 108 |
Distillation of multiple copies of a pure state | p. 108 |
Analogy with the Carnot Cycle | p. 110 |
Properties of entanglement measures | p. 111 |
Entanglement of pure states | p. 113 |
Entanglement of mixed states | p. 113 |
Measures of entanglement derived from relative entropy | p. 117 |
Classical information and entanglement | p. 121 |
Entanglement and thermodynamics | p. 123 |
Summary | p. 128 |
Quantum Computation | |
Quantum algorithms | p. 131 |
Computational complexity | p. 131 |
Deutsch's algorithm | p. 133 |
Deutsch's algorithm and the Holevo bound | p. 135 |
Oracles | p. 136 |
Grover's search algorithm | p. 137 |
Quantum factorization | p. 140 |
Factorization | p. 141 |
The quantum Fourier transform | p. 142 |
Phase estimation | p. 144 |
Summary | p. 145 |
Entanglement, computation and quantum measurements | p. 146 |
Optimization of searches using entanglement | p. 147 |
Model for quantum measurement | p. 149 |
Correlations and quantum measurement | p. 151 |
The ultimate limits of computation: the Bekenstein bound | p. 157 |
Summary | p. 158 |
Quantum error correction | p. 160 |
Introduction | p. 160 |
A simple example | p. 160 |
General conditions | p. 162 |
Reliable quantum cumputation | p. 165 |
Quantum error correction considered as a Maxwell's demon | p. 167 |
Pure states | p. 171 |
Mixed states | p. 172 |
Summary | p. 173 |
Outlook | p. 175 |
Bibliography | p. 179 |
Index | p. 181 |
Table of Contents provided by Ingram. All Rights Reserved. |
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