Quantum Approach to Informatics

CONTENTS

PREFACE

1 INTRODUCTION

1.1 Background

1.2 Quantum Information Unit

1.3 Representation of the Qubit

1.3.1 Bloch Sphere

1.3.2 Poincaré Sphere

1.4 The Appetizer: Secure Communication

1.5 References

2 QUANTUM THEORY

2.1 Quantum Mechanics

2.1.1 Structure of Quantum Theory

2.1.2 Quantum Ensembles

2.2 Nonlocality of Quantum Mechanics

2.2.1 Nonsignaling by Quantum Observations

2.2.2 No Cloning of Quantum States

2.2.3 Teleportation

2.2.4 Bell Inequalities

2.2.5 GHZ States and Reality

2.3 The Process of Measurement

2.3.1 Introducing the Meter

2.3.2 Measurement Transformation

2.3.3 Observation on Nonorthogonal States

2.3.4 Special Cases

2.4 Introduction of Irreversibility

2.4.1 Master Equation

2.4.2 Unraveling the Master Equation

2.4.3 Continuous Measurements

2.4.4 Completely Positive Maps

2.5 References

3 QUANTUM COMMUNICATION AND INFORMATION

3.1 Classical Communication

3.1.1 Information Theory

3.1.2 Coding Theory

3.2 Quantum Communication

3.2.1 Quantum Information

3.2.2 Quantum Channel

3.2.3 Use of Generalized Measurements

3.2.4 Neumark Extension

3.3 Distance Between States

3.3.1 Trace Distance

3.3.2 Fidelity

3.3.3 Relative Entropy

3.4 References

4 QUANTUM COMPUTING

4.1 Logic Operations

4.1.1 Classical Logic Operations

4.1.2 Quantum Logic Functions

4.1.3 Simple Quantum Operations

4.1.4 The Deutsch Problem

4.2 The Computer

4.2.1 Classical Universal Computer

4.2.2 Computational Complexity

4.2.3 Quantum Computer

4.2.4 Quantum Computing Circuits

4.2.5 Universal Quantum Gates

4.2.6 ...