Quantum Communication Networks (Foundations in Signal Processing, Communications and Networking, 23)

✍ Scribed by Riccardo Bassoli, Holger Boche, Christian Deppe, Roberto Ferrara, Frank H. P. Fitzek, Gisbert Janssen, Sajad Saeedinaeeni

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 239
• Category: Library

✦ Synopsis

This book provides a tutorial on quantum communication networks. The authors discuss current paradigm shifts in communication networks that are needed to add computing and storage to the simple transport ideas of prevailing networks. They show how these ‘softwarized’ solutions break new grounds to reduce latency and increase resilience. The authors discuss how even though these solutions have inherent problems due to introduced computing latency and energy consumption, the problems can be solved by hybrid classical-quantum communication networks. The book brings together quantum networking, quantum information theory, quantum computing, and quantum simulation.

✦ Table of Contents

Preface
Acknowledgments
Contents
About the Authors
1 Introduction
1.1 The Evolution of Classical Communication Networks
1.2 Toward Quantum Communication Networks
1.3 Structure of the Book
2 Fundamental Background
2.1 Preliminaries on Quantum Mechanics
2.1.1 Postulates of Quantum Mechanics
2.1.2 Formulation of Quantum Mechanics
2.1.3 Composite Systems and Entanglement
2.1.4 Composite Observables
2.2 Noise in Quantum Systems
2.2.1 Density Matrix
2.2.2 The Bloch Sphere of a Qubit
2.2.3 Composite Systems
2.2.4 Quantum Channels
2.3 Measurements
2.4 Quantum Information
2.4.1 Statistical Theories
2.4.1.1 Convexity
2.4.2 Distance Measures
2.4.3 Quantum Entropy
2.5 Bell Nonlocality
2.5.1 Nonlocal Games
2.6 Classical and Quantum Mechanics
3 Quantum Computing and Programming
3.1 Universal Gate Sets
3.1.1 Quantum Circuit Model
Tensor Networks
3.1.2 Quantum Universal Gate Sets
3.2 Computational Complexity
3.3 The Quantum Fourier Transform
3.4 Oracle and Promise Problems
3.5 Interference: Balanced Functions
3.5.1 Deutsch Algorithm
3.5.2 Deutsch–Jozsa Algorithm
3.5.3 Bernstein–Vazirani Algorithm
3.6 Measurements: Hidden Subgroups
3.6.1 Co-set States
3.6.2 Period-Finding Algorithm
3.6.3 Simon's Algorithm
3.7 Phase Estimation
3.8 Application: Order Finding and RSA
3.9 Grover's Search
3.10 Quantum Simulation
3.11 Other Applications
3.12 Immediate Future
4 Quantum Information Theory
4.1 Dense Coding and Teleportation
4.2 Quantum Hypotheses Testing: Quantum Stein's Lemma
4.3 Source Compression for Memoryless Quantum Sources
Some Properties of the von Neumann Entropy
4.4 Message Transmission over Quantum Channels
4.4.1 The Discrete Memoryless Classical-Quantum Channel
4.4.2 The Discrete Memoryless Quantum Channel
4.4.3 Some Properties of the Holevo Quantity
4.5 Entanglement-Assisted Classical Communication
4.6 Information-Theoretic Security and CQQ Wiretap Model
4.7 Public and Secure Identification
4.7.1 Identification via CQ Channels
4.7.2 Secure Identification
4.8 Channel Uncertainty: Compound and Arbitrarily Varying Models
4.8.1 Notations and Conventions
4.8.2 Simultaneous Transmission of Classical and Quantum Information
4.8.2.1 The Compound Quantum Channel
4.8.2.2 Classically Enhanced Entanglement Transmission (CET)
4.8.2.3 Classically Enhanced Entanglement Generation (CEG)
4.8.2.4 The Arbitrarily-Varying Quantum Channel
4.8.2.5 The Fully-Quantum Arbitrarily-Varying Channel
4.8.3 Compound Quantum Broadcast Channel with Confidential Messages
4.8.3.1 Basic Definitions and Main Results
4.8.3.2 BCC and TPC Capacities of Compound Quantum Broadcast Channels
4.8.4 Robust Secure Message Transmission over the Wiretap Channel with a Jammer
4.8.5 Robust Identification over CQ Channel for Public and Secure Communication
4.8.5.1 Identification Over Compound CQ Channel
4.8.5.2 Identification over the CQQ Wiretap Channel
4.8.5.3 Identification in the Presence of a Jammer
4.8.5.4 Secure Identification in the Presence of a Jammer
5 Quantum Error Correction
5.1 Forward Error Correction Codes
5.2 Bit and Phase Errors: Quantum Repetition Code
5.3 Single Pauli Error: Shor's Error Correction Code
5.4 Error Correction Condition and Code Distance
5.5 Linear Codes and Stabilizer Codes
5.5.1 Linear Block Codes
5.5.2 Stabilizer Codes
5.5.3 Calderbank–Shor–Steane (CSS) Codes
5.6 Universal Logical-Gate Sets
5.7 Topological Stabilizer Codes
5.7.1 The Toric Code
5.7.2 Color Codes
6 Quantum Communication Networks: Design and Simulation
6.1 Distillation in Quantum Repeaters
6.2 Taxonomy of Quantum Repeaters
6.3 Storage in Quantum Repeaters
6.4 Entanglement Distribution
6.5 Multiple-Access Channel in Quantum Communication Networks
6.6 Classical Simulation of Quantum Communication Networks
6.6.1 SimulaQron
6.6.2 NetSquid
6.6.3 QuNetSim
6.6.4 SQUANCH
6.6.5 SeQUeNCe
6.6.6 QuISP
6.6.7 LIQUliq
7 Quantum Communication Networks: Final Considerations and Use Cases
References
Index