Protecting Information From Classical Error Correction to Quantum Cryptography

ISBN-10: 0521534763

ISBN-13: 9780521534765

Edition: 2006

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Description: In the transition of information storage, preventing noise and/or eavesdropping is essential. This undergraduate introduction to quantum computing focuses on error correction and cryptography, providing a context in which ideas about mathematics, computer science and physics meet together.

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Book details

List price: $54.99
Copyright year: 2006
Publisher: Cambridge University Press
Publication date: 7/31/2006
Binding: Paperback
Pages: 304
Size: 5.98" wide x 8.98" long x 0.59" tall
Weight: 0.946
Language: English

Susan Loepp is an Associate Professor of Mathematics in the Department of Mathematics and Statistics at Williams College. Her research is in commutative algebra, focusing on completions of local rings.

William K. Wootters, a Fellow of the American Physical Society, is the Barclay Jermain Professor of Natural Philosophy in the Department of Physics at Williams College. He does research on quantum entanglement and other aspects of quantum information theory.

Preface
Acknowledgments
Cryptography: An Overview
Elementary Ciphers
Enigma
A Review of Modular Arithmetic and Z[subscript n]
The Hill Cipher
Attacks on the Hill Cipher
Feistel Ciphers and DES
A Word about AES
Diffie-Hellman Public Key Exchange
RSA
Public Key Exchanges with a Group
Public Key Exchange Using Elliptic Curves
Quantum Mechanics
Photon Polarization
Linear polarization
Review of complex numbers
Circular and elliptical polarization
General Quantum Variables
Composite Systems
Measuring a Subsystem
Other Incomplete Measurements
Quantum Cryptography
The Bennett-Brassard Protocol
The No-Cloning Theorem
Quantum Teleportation
An Introduction to Error-Correcting Codes
A Few Binary Examples
Preliminaries and More Examples
Hamming Distance
Linear Codes
Generator Matrices
Dual Codes
Syndrome Decoding
The Hat Problem
Quantum Cryptography Revisited
Error Correction for Quantum Key Distribution
Introduction to Privacy Amplification
Eve knows a fixed number of elements of the bit string
Eve knows the parities of certain subsets of the bit string
The general case
Generalized Reed-Solomon Codes
Definitions and Examples
A Finite Field with Eight Elements
General Theorems
A Generator Matrix for a GRS Code
The Dual of a GRS Code
Quantum Computing
Introduction
Quantum Gates
The Deutsch Algorithm
A Universal Set of Quantum Gates
Number Theory for Shor's Algorithm
Finding the Period of f(x)
Estimating the Probability of Success
Efficiency of Factoring
Introduction to Quantum Error Correction
An X-correcting code
A Z-correcting code
The Shor code
Fields
A Glossary of Linear Algebra Definitions and Theorems
Tables for the Alphabet
References
Index
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