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Advances in systems analysis, software engineering, and high performance computing book series

Quantum Entanglement

Javid Naikoo

Published Jul 26, 2024• 0 citations
Publisher

Abstract

The aim of this chapter is to introduce the reader to various aspects of quantum entanglement. A detailed summary of the jargon of important mathematical notions, and concepts used in entanglement theory is provided. Various methods of entanglement generation are discussed followed by an introduction to the methods of detection and quantification of quantum entanglement in terms of various witnesses and measures. A brief account of some well-known applications of quantum entanglement is presented. Finally, a set of problems with solutions is provided, illustrating various important concepts discussed in the chapter.

DOI
10.4018/978-1-7998-9522-0.ch004

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The aim of this chapter is to introduce the reader to various aspects of quantum entanglement. A detailed summary of the jargon of important mathematical notions, and concepts used in entanglement theory is provided. Various methods of entanglement generation are discussed followed by an introduction to the methods of detection and quantification of quantum entanglement in terms of various witnesses and measures. A brief account of some well-known applications of quantum entanglement is presented. Finally, a set of problems with solutions is provided, illustrating various important concepts discussed in the chapter.
Entanglement finds wide application in the development of quantum information theory. After reviewing states in classical mechanics, this chapter discusses the fundamental aspects of characterization of quantum entanglement like the definition, the detection, the classification and quantification of entanglement. The density operator is used to describe the state of a quantum system in a more general way than provided by the state vector of the Hilbert space. Multipartite entanglement theory is much complex compared to the bipartite case. One cannot generalize the results of bipartite entanglement to multipartite entanglement. The Peres criterion known as positive partial transpose criterion is an important criterion to find the separability of mixed states at least for low-dimensional systems. B.W. Terhal introduced the term entanglement witnesses for operators detecting quantum entanglement states. It is found that any entangled state can be detected by some entanglement witnesses.
Quantum entanglement, a fundamental concept in quantum physics, has been elucidated through the development of Bell’s inequalities. Recent advancements have enabled controlled manipulation and measurement of entangled quantum states. This chapter provides a concise overview of entanglement’s mathematical underpinnings, its manipulation, and quantification. Special attention is given to quantification methods and their implications in quantum information. Key principles and measures are presented to facilitate a foundational understanding. Readers are encouraged to supplement this overview with comprehensive review articles and primary literature for further insights.
This chapter is intended for nonpractitioners in the field with a technical background but not necessarily at the doctoral level and so minimizes equations and the more specialized jargon. The chapter starts with a brief history of quantum mechanics. The important basic concepts of quantum mechanics are discussed, and some commonly used terms and common quantum experiments are introduced. The difference between quantum and “classical” physics is discussed. The role of quantum theory in modern physics is explained. A number of applications of quantum phenomena are discussed with some emphasis on the three areas of the US National Quantum Initiative: quantum computing, quantum sensing, and quantum communications. Finally, the various interpretations of quantum mechanics with respect to its meanings for physical reality are touched upon. At this writing, quantum technologies are receiving increased emphasis and funding in several areas both in the US and several other nations, which is discussed.
The real-world systems of quantum cryptography represent an advancement in the field of communication, wherein the advantages offered by quantum mechanics are used to minimize security threats which are handled with classical computers. This chapter starts with introducing some concepts to the reader about Quantum Cryptography, starting with an overview of classical Cryptography and its limitations in this new era of quantum computing technologies. Certain aspects of quantum mechanics like superposition, quantum entanglement, no-cloning theorem, and their applications for Quantum Key Distribution are also studied. This followed a thorough analysis of key protocols BB84 and E91 to unmask their strengths in securing superior security. Security threats associated with quantum-cryptographic systems and their corresponding provable level of security are considered to strengthen the notion of quantum cryptography as opposed to methods of classical cryptography. The corresponding characteristics of such quantum-cryptographic methods are also discussed for their application in proper targets. By the end of this chapter, we will attempt to explain the conception of some complications regarding quantum mechanics, and how they are now of use in modern practices of quantum cryptography and why such techniques are needed at all.
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This chapter explores the rapidly developing field of quantum computing, which essentially devises the power to change science and technology. After an introductory outline, the fundamental ideas of quantum computing are covered, setting it apart from classical computing. The chapter then goes on to describe the features of a quantum computing system, highlighting its unique traits and possible advantages. The reliance on complex numbers and advanced mathematics is a central point of quantum computing [ 1 ]. Fundamental mathematical concepts are important to understand the quantum algorithms, which are explained in more detailed way. In quantum computing, the main idea is that quantum bits can have several states. The quality of quantum processing is extensively explored in this chapter. The chapter also covers a range of quantum computing techniques, highlighting their resourceful methods for tackling problems. Finally, the uses of quantum computing and its influence in many areas, such as optimization, materials research, and cryptography, are described and analyzed. This ample introduction will provide readers with thoughtful principles and the mathematical and practical significance of quantum computing.