1st Edition

Introduction to Quantum Physics and Information Processing




ISBN 9781482238112
Published August 24, 2015 by CRC Press
270 Pages 88 B/W Illustrations

USD $105.00

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Book Description

An Elementary Guide to the State of the Art in the Quantum Information Field

Introduction to Quantum Physics and Information Processing guides beginners in understanding the current state of research in the novel, interdisciplinary area of quantum information. Suitable for undergraduate and beginning graduate students in physics, mathematics, or engineering, the book goes deep into issues of quantum theory without raising the technical level too much.

The text begins with the basics of quantum mechanics required to understand how two-level systems are used as qubits. It goes on to show how quantum properties are exploited in devising algorithms for problems that are more efficient than the classical counterpart. It then explores more sophisticated notions that form the backbone of quantum information theory.

Requiring no background in quantum physics, this text prepares readers to follow more advanced books and research material in this rapidly growing field. Examples, detailed discussions, exercises, and problems facilitate a thorough, real-world understanding of quantum information.

Table of Contents

Preliminaries
Introduction
Bits and Qubits
Properties of Qubits
Practical Considerations
References for Further Reading

A Simple Quantum System
The Stern–Gerlach Experiment
Quantum State: Basis States
An Experiment to Illustrate Superpositions
Interference and Complex Amplitudes

Theoretical Framework
The Essentials of Quantum Mechanics
The State Space
Observables
Measurement
Evolution
Composite Systems
Properties of Qubits
The Bloch Sphere Representation of a Qubit
Cloning and Deleting
Distinguishability of Qubit States
Entanglement

Mixed States, Open Systems, and the Density Operator
The Density Operator
Quantum Mechanics with Density Operators
Composite Systems

Computation Models and Computational Complexity
Computability and Models for Computation
The Circuit Model and Universal Gates
Reversible Computation
Resources and Computational Complexity

Quantum Computation
Quantum Gates and Circuits
Single Qubit Gates
Multi-Qubit Gates
Quantum Function Evaluation
Universal Quantum Gates
Comments on Measurement

Quantum Algorithms
The Deutsch Algorithm
The Bernstein–Vazirani Algorithm
Simon’s Algorithm
Quantum Fourier Transform and Applications
Definition of the QFT from Discrete Fourier Transform
Grover’s Search Algorithm

Quantum Information
Information and Communication
Entanglement as a Resource
Quantum Dense Coding
Quantum Cryptography
Quantum Key Distribution
Information Reconciliation and Privacy Amplification

Quantum Error Correction
3-Qubit Repetition Code for Bit Flips
Phase Flip Code
9-Qubit Shor Code
Discretization of Quantum Errors
The 5-Qubit Code
The 7-Qubit Code

Characterization of Quantum Information
Measures of Information
The Von Neumann Entropy
Distance Measures
Entanglement Measures

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Author(s)

Biography

Radhika Vathsan is an associate professor in the Department of Physics at BITS Pilani, Goa Campus. She earned a PhD in theoretical physics from the Institute of Mathematical Sciences Chennai and did her postdoc work at Harish Chandra Research Institute Allahabad. Her research interests include mathematical physics, many-body physics, high-energy physics, quantum computation and information, and foundations of quantum mechanics.