Introduction to Quantum Physics and Information Processing: 1st Edition (Hardback) book cover

Introduction to Quantum Physics and Information Processing

1st Edition

By Radhika Vathsan

CRC Press

270 pages | 88 B/W Illus.

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pub: 2015-08-24
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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

About the Author

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.

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT004000
MATHEMATICS / Arithmetic
SCI055000
SCIENCE / Physics
SCI057000
SCIENCE / Quantum Theory