Quantum Zero-Error Information Theory

ISBN-13: 9783319427935 / Angielski / Twarda / 2016 / 189 str.

Elloa B. Guedes; Francisco Marcos De Assis; Rex Antonio Da Costa Medeiros

Opis

This book aims at presenting the field of Quantum Information Theory in an intuitive, didactic and self-contained way, taking into account several multidisciplinary aspects. Therefore, this books is particularly suited to students and researchers willing to grasp fundamental concepts in Quantum Computation and Quantum Information areas.The field of Quantum Information Theory has increased significantly over the last three decades. Many results from classical information theory were translated and extended to a scenario where quantum effects become important. Most of the results in this area allows for an asymptotically small probability of error to represent and transmit information efficiently. Claude E.Shannon was the first scientist to realize that error-free classical information transmission can be accomplished under certain conditions. More recently, the concept of error-free classical communication was translated to the quantum context. The so-called Quantum Zero-Error Information Theory completes and extends the Shannon Zero-Error Information Theory.

Recenzje

"The book is a work on quantum zero-error information theory that covers fundamental material ... in a highly pedagogical way, making it an important reference for courses on information theory, quantum information theory and quantum computation. ... the book is also of major interest for anyone in mathematical, physics, computer science and engineering communities that develop research on quantum technologies ... . a well-organized pedagogical work that can be used by students, lecturers and researchers on quantum zero-error information theory." (Carlos Pedro Gonçalves, zbMATH 1364.81007, 2017)

Spis treści

0. Introduction

1. Fundamentals of Quantum Mechanics

a) Representing information

b) Processing information

c) Measuring information

d) Density operator

e) Quantum mechanics postulates

f) POVM Measurement

g) Further reading

2. Fundamentals of Information Theory

a) Classical Information Theory

b) Quantum Information Theory

c) Further reading

3. Classical Zero-Error Information Theory

a) Historical background

b) Zero-error capacity

c) Representation in graphs

d) Lovász theta function

e) Zero-error capacity of joint systems

f) Further reading

4. Quantum Zero-Error Information Theory

a) Quantum zero-error capacity

b) Representation in graphs

c) Relations with Holevo-Schumacher-Westmoreland capacity

d) Further reading

5. Quantum Zero-Error Secrecy Capacity

a) Decoherence-Free Subspaces and Subsystems

b) Quantum Secrecy Capacity

c) Defining the Quantum Zero-Error Secrecy Capacity

d) Representation in graphs

e) Security Analysis

f) Further reading

6. Zero-Error Accessible Information of a Quantum Source

a) Accessible Information of Quantum Source

b) Zero-Error Accessible Information of a Quantum Source

c) Representation in graphs

d) Further reading

7. Recent Developments in Quantum Zero-Error Information Theory

a) Alternative definitions

b) Superactivation of Quantum Zero-Error Capacity

c) Practical implementations

d) Further reading

Blurb

This book aims at presenting the field of Quantum Information Theory in an intuitive, didactic and self-contained way, taking into account several multidisciplinary aspects. Therefore, this book is particularly suited to students and researchers willing to grasp fundamental concepts in Quantum Computation and Quantum Information areas.

The field of Quantum Information Theory has evolved significantly over the last three decades. Many results from classical information theory were translated and extended to a scenario where quantum effects become important. Most of the results in this area allows for an asymptotically small probability of error to represent and transmit information efficiently. Claude E.Shannon was the first scientist to realize that error-free classical information transmission can be accomplished under certain conditions. More recently, the concept of error-free classical communication was translated to the quantum context. The so-called Quantum Zero-Error Information Theory completes and extends the Shannon Zero-Error Information Theory.