Quantum Networks

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.

Quantum networks build on entanglement and quantum measurement to achieve tasks that are beyond the reach of classical systems. Using quantum effects, we can detect the presence of eavesdroppers, raise the sensitivity of scientific instruments such as telescopes, or teleport quantum data from one location to another. Long-distance entanglement can be used to execute important tasks such as Byzantine agreement and leader election in fewer rounds of communication than classical systems, improving the efficiency of operations that are critical in distributed systems.

Quantum Networks is focused on density matrix theory cast into a product operator representation, particularly adapted to describing networks of finite state subsystems. This approach is important for understanding non-classical aspects such as single subsystem and multi-subsystem entanglement. An intuitive picture evolves of how these features are generated and destroyed by interactions with the environment. This second edition has been revised and enlarged. For better clarity the text has been partly reorganized and figures and formulae are presented in a more attractive way.

Faithful communication is a necessary precondition for large-scale quantum information processing and networking, irrespective of the physical platform. Thus, the problems of quantum-state transfer and quantum-network engineering have attracted enormous interest over the last years, and constitute one of the most active areas of research in quantum information processing. The present volume introduces the reader to fundamental concepts and various aspects of this exciting research area, including links to other related areas and problems. The implementation of state-transfer schemes and the engineering of quantum networks are discussed in the framework of various quantum optical and condensed matter systems, emphasizing the interdisciplinary character of the research area. Each chapter is a review of theoretical or experimental achievements on a particular topic, written by leading scientists in the field. The volume aims at both newcomers as well as experienced researchers.

With the fast pace of developments in quantum technologies, it is more than ever necessary to make the new generation of students in science and engineering familiar with the key ideas behind such disruptive systems. This book intends to fill such a gap between experts and non-experts in the field by providing the reader with the basic tools needed to understand the latest developments in quantum communications and its future directions. This is not only to expand the audience knowledge but also to attract new talents to this flourishing field. To that end, the book as a whole does not delve into much detail and most often suffices to provide some insight into the problem in hand. The primary users of the book will then be students in science and engineering in their final year of undergraduate studies or early years of their post-graduate programmes.

The focus here is on density matrix theory cast into a representation - SU(n) algebra - since this is particularly adapted to describing networks of quasi-molecular subsystems. This approach allows an understanding of how classical properties emerge within a quantum mechanical world and how non-classical features survive in a classical environment. The authors introduce and discuss non-classical aspects such as single-particle and multi-particle coherence such that a picture evolves of how these features are generated and destroyed by interactions with the environment. The outcome is a description of how the dynamics of individual quantum systems are interrelated with information dynamics.

Quantum Communication, Quantum Networks, and Quantum Sensing represents a self-contained introduction to quantum communication, quantum error-correction, quantum networks, and quantum sensing. It starts with basic concepts from classical detection theory, information theory, and channel coding fundamentals before continuing with basic principles of quantum mechanics including state vectors, operators, density operators, measurements, and dynamics of a quantum system. It continues with fundamental principles of quantum information processing, basic quantum gates, no-cloning and theorem on indistinguishability of arbitrary quantum states. The book then focuses on quantum information theory, quantum detection and Gaussian quantum information theories, and quantum key distribution (QKD). The book then covers quantum error correction codes (QECCs) before introducing quantum networks. The book concludes with quantum sensing and quantum radars, quantum machine learning and fault-tolerant quantum error correction concepts. Integrates quantum information processing fundamentals, quantum communication, quantum error correction, quantum networks, QKD, quantum sensing, and quantum machine learning Provides in-depth exposition on the design of quantum error correction circuits, quantum communications systems, quantum networks, and quantum sensing systems Shows how to design the information processing circuits, stabilizer codes, CSS codes, entanglement-assisted quantum error correction codes Describes quantum machine learning

A highly interdisciplinary overview of the emerging topic of the Quantum Internet. Current and future quantum technologies are covered in detail, in addition to their global socio-economic impact. Written in an engaging style and accessible to graduate students in physics, engineering, computer science and mathematics.