Quantum Information, Computation and Cryptography

An Introductory Survey of Theory, Technology and Experiments

By: Fabio Benatti (Editor), Mark Fannes (Editor), Roberto Floreanini (Editor)

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Paperback | 21 September 2010

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362 Pages

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This multi-authored textbook addresses graduate students with a background in physics, mathematics or computer science. No research experience is necessary.

Consequently, rather than comprehensively reviewing the vast body of knowledge and literature gathered in the past twenty years, this book concentrates on a number of carefully selected aspects of quantum information theory and technology.

Given the highly interdisciplinary nature of the subject, the multi-authored approach brings together different points of view from various renowned experts, providing a coherent picture of the subject matter.

The book consists of ten chapters and includes examples, problems, and exercises. The first five present the mathematical tools required for a full comprehension of various aspects of quantum mechanics, classical information, and coding theory. Chapter 6 deals with the manipulation and transmission of information in the quantum realm. Chapters 7 and 8 discuss experimental implementations of quantum information ideas using photons and atoms. Finally, chapters 9 and 10 address ground-breaking applications in cryptography and computation.

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Hilbert Space Methods for Quantum Mechanics	p. 1
Hilbert Spaces	p. 1
Postulates of Quantum Mechanics	p. 13
Some Applications	p. 25
References	p. 31
Classical Information Theory	p. 33
Entropy	p. 33
Source Coding	p. 44
Channel Coding	p. 53
Bibliographical Notes	p. 64
References	p. 64
Quantum Probability and Quantum Information Theory	p. 65
Introduction	p. 65
Why Classical Probability Does Not Suffice	p. 67
Toward a Mathematical Model	p. 74
Quantum Probability	p. 80
Operations on Probability Spaces	p. 88
Quantum Impossibilities	p. 98
Quantum Novelties	p. 104
References	p. 108
Bipartite Quantum Entanglement	p. 109
Introduction	p. 109
Bipartite Entanglement	p. 111
Entanglement Detection	p. 120
Complete Positivity, Open Quantum Systems, and Entanglement	p. 134
References	p. 148
Field-Theoretical Methods	p. 151
Introduction	p. 151
The Quantum Harmonic Oscillator	p. 152
Quantum Bosonic Fields	p. 159
Coherent and Thermal States for Bosons	p. 166
Second Quantization of Fermions	p. 172
Further Reading	p. 174
References	p. 174
Quantum Entropy and Information	p. 175
Introduction	p. 175
Preliminaries	p. 176
Rudiments of Classical Information Theory	p. 179
Quantum Entropy	p. 185
Data Compression in Quantum Information Theory	p. 187
Quantum Channels	p. 193
Accessible Information and the Holevo Bound	p. 200
References	p. 214
Photonic Realization of Quantum Information Protocols	p. 215
Introduction	p. 215
Photon Entanglement	p. 220
Optical Realizations of Quantum Information Protocols	p. 232
Optical Quantum Computation Protocols	p. 233
Quantum Communication	p. 237
References	p. 248
Physical Realizations of Quantum Information	p. 253
Introduction	p. 253
A Single Qubit in Interaction with the Radiation Field	p. 256
Qubit Entanglement Through the Jaynes-Cummings Interaction	p. 268
References	p. 274
Quantum Cryptography	p. 277
Introduction	p. 277
Classical Cryptography	p. 278
Quantum Cryptography	p. 279
Eavesdropping Strategies	p. 287
Unconditional Security of BB84	p. 291
Defense Against Eavesdropping with Photon Number Splitting (PNS) Attacks	p. 301
Classical Upper Bounds on the Secret Key Rate	p. 302
The Role of Entanglement in QKD	p. 304
Problems/Exercises	p. 307
References	p. 308
Quantum Algorithms	p. 309
Notations	p. 310
The Quantum Circuit Model	p. 312
First Algorithms	p. 316
The Quantum Fourier Transform	p. 319
Deutsch-Josza and Simon's Algorithms	p. 323
Factoring in Polynomial Time	p. 326
The Hidden Subgroup Problem	p. 331
Grover's Algorithm for Unstructured Search	p. 334
Developments	p. 338
References	p. 340
Index	p. 343
Table of Contents provided by Ingram. All Rights Reserved.

Quantum Information, Computation and Cryptography

An Introductory Survey of Theory, Technology and Experiments

At a Glance

Paperback

Shipping

How to return your order

Defective items

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