1st Edition

Introduction to Quantum Physics and Information Processing

By Radhika Vathsan Copyright 2016
    270 Pages 88 B/W Illustrations
    by CRC Press

    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.

    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

    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.