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Chapman & Hall/CRC eBooks

Essentials From Quantum Physics

Binayak Samadder Choudhury, Soumen Samanta

Published Dec 10, 2025• 0 citations
Publisher

Abstract

This chapter contains concepts from quantum physics which are essential for the understanding of the teleportation protocols. Qubit system is discussed separately along with the laws of its evolution. Quantum gates and quantum circuits are described. The description is limited to the technical and conceptual requirements for understanding the materials in the book. For an extensive appraisal of the topics included in this chapter, [ 6 , 12 , 15 , 32 , 35 , 55 , 77 , 81 , 107 , 113 , 117 , 134 , 139 , 140 , 149 , 163 , 171 ] are helpful references.

DOI
10.1201/9781003561439-3

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This chapter contains concepts from quantum physics which are essential for the understanding of the teleportation protocols. Qubit system is discussed separately along with the laws of its evolution. Quantum gates and quantum circuits are described. The description is limited to the technical and conceptual requirements for understanding the materials in the book. For an extensive appraisal of the topics included in this chapter, [ 6 , 12 , 15 , 32 , 35 , 55 , 77 , 81 , 107 , 113 , 117 , 134 , 139 , 140 , 149 , 163 , 171 ] are helpful references.
Quantum mechanics — central not only to physics, but also to chemistry, materials science, and other fields — is notoriously abstract and difficult. This book is a concise, explanatory book that focuses on the fundamental structure, concepts, and methods of quantum mechanics, filling the gap between introductory and advanced studies, between popularizations and technical treatises. Although physical understanding is emphasized, the mathematical sophistication necessary to achieve that understanding is also developed. A modern perspective is adopted throughout, the goal being to gain entry into quantum mechanics as used by practicing scientists. This perspective includes a focus on quantum states generally, not just wavefunctions, and a strong emphasis on Dirac notation. Many standard topics are developed, such as the Schrödinger equation, quantum states, operators, and matrix mechanics. Some non-standard topics are also discussed, such as the complex nature of quantum states, and various interpretations of the uncertainty relations. Discussion of applications is limited, and focuses on elucidating the structure of quantum mechanics.
Since its emergence in the early twentieth century, quantum theory has become the fundamental physical paradigm, and is essential to our understanding of the world. Providing a deeper understanding of the microscopic world through quantum theory, this supplementary text reviews a wider range of topics than conventional textbooks. Emphasis is given to modern entanglement, quantum teleportation, and Bose-Einstein condensation. Macroscopic quantum effects of practical relevance, for example superconductivity and the quantum Hall effect, are also described. Looking to the future, the author discusses the exciting prospects for quantum computing. Physical, rather than formal, explanations are given, and mathematical formalism is kept to a minimum so readers can understand the concepts more easily. Theoretical discussions are combined with a description of the corresponding experimental results. This book is ideal for undergraduate and graduate students in quantum theory and quantum optics.
In this chapter, the mathematics that are used in the discussion of the teleportation protocols are provided. Hilbert spaces, which are linear spaces with appropriate geometries brought about by introducing inner products, form the mathematical framework of the above-mentioned discussion. These spaces along with the relevant operators for describing the required part of quantum physics are presented here. For extensive studies on the topics included in this chapter, the references [ 33 , 34 , 62 , 78 , 113 , 136 , 152 , 156 , 170 , 189 ] are useful.
Abstract Quantum mechanics is conceptually challenging and requires mathematics, but it is an essential basis for understanding nanoscience. Though simplified, the material in this chapter covers what might be learned in an entire semester, so if you have not been exposed to the subject before, panic would be a reasonable reaction! The chapter is long because it (almost) serves as a stand-alone guide to the subject (taken in conjunction with Appendix C). This outline lists the essential “take-home” points needed to follow the rest of the book. If you grasp these, you can always come back to this chapter later for more background.
Scope of this book Quantum mechanics is a difficult subject, and this book is intended to help the reader overcome the main difficulties in the way to understanding it. The first part of the book, Chs. 2–16, contains a systematic presentation of the basic principles of quantum theory, along with a number of examples which illustrate how these principles apply to particular quantum systems. The applications are, for the most part, limited to toy models whose simple structure allows one to see what is going on without using complicated mathematics or lengthy formulas. The principles themselves, however, are formulated in such a way that they can be applied to (almost) any nonrelativistic quantum system. In the second part of the book, Chs. 17–25, these principles are applied to quantum measurements and various quantum paradoxes, subjects which give rise to serious conceptual problems when they are not treated in a fully consistent manner. The final chapters are of a somewhat different character. Chapter 26 on decoherence and the classical limit of quantum theory is a very sketchy introduction to these important topics along with some indication as to how the basic principles presented in the first part of the book can be used for understanding them. Chapter 27 on quantum theory and reality belongs to the interface between physics and philosophy and indicates why quantum theory is compatible with a real world whose existence is not dependent on what scientists think and believe, or the experiments they choose to carry out. The Bibliography contains references for those interested in further reading or in tracing the origin of some of the ideas presented in earlier chapters.