Entropy is a central concept in both classical and quantum information theory, measuring the uncertainty and the information content in the state of a physical system. Lecture notes on quantum information and computation. Figure 1 is just one example of a huge variety of quantum circuits that are used to compactly. Recently, quantum information theory has been developing through a fusion of results from various research fields. Quantum information theory is the study of the achievable limits of information processing within quantum mechanics. For instance, adiabatic quantum computing finds the minimum of a multivariate function by a controlled physical process using the adiabatic theorem farhi et al. Quantum information theory is a generalization of classical information theory to use quantummechanical particles and interference. Quantum information processing is a young and rapidly growing field of research at the intersection of physics, mathematics, and computer science. He argues for an ontologically deflationary account of the nature of quantum information, which is grounded in a revisionary analysis of the concepts of information. In its extreme form, the thought is that information is perhaps the fundamental category from which all else. It is assumed that the reader is already familiar with the most. Quantum information an introduction masahito hayashi.
Sep 10, 2018 in 2017 reinhard werner gave a series of lectures on the mathematical methods of quantum information theory at the leibniz universitat hannover. This thesis is a contribution to the debate on the implications of quantum information theory for the foundational problems of quantum mechanics. They can be used freely, but please understand that they are just lecture notes and undoubtedly contain errors. The underlying quantum mechanics leads to important differences between quantum and classical information theory. Abstract quantum information theory provides a foundation for such topics as quantum cryptography, quantum errorcorrection and quantum teleportation. Therefore, since the physical world is fundamentally quantum mechanical, the foundations of information theory and computer science should be sought in quantum physics. Such a single unit su ces, because di erent forms of.
The corresponding unit of quantum information is called the quantum bit or qubit. The course will start with a short introduction to some of the basic concepts and tools of classical information theory, which will prove useful in the study of quantum information theory. In retrospect, this development seems somewhat belated. Clearly explaining the necessary mathematical basis, it merges key topics from both informationtheoretic and quantum mechanical viewpoints and provides lucid explanations of the basic results. Developing the subject from the ground up it covers classical results as well as major advances of the past decade. Degree competences to which the subject contributes.
But because we are short of time im anxious to move on to quantum computation, i wont be able to cover this subject in as much depth as i would have liked. This category has the following 2 subcategories, out of 2 total. Quantum information theory qita generalization of shannons classical information theory to account for the quantum physical nature of information, information carriers, channels, and measurementsis a fast developing field, which has matured immensely over the past two decades or so. Quantum information theory an overview sciencedirect. Mathematical methods of quantum information theory, lecture 1. Prerequisites for understanding the content in this book are a solid background in probability theory and linear algebra.
Ideas of quantum mechanics, information, and the relationships between them, however. A short course in quantum information theory springer, 2007. In this sense a letter xchosen from the ensemble carries, on the average, hx bits of. In addition the book consistent quantum theory by r. The national institute of standards and technology nist has contributed to much of its history and is helping to shape its future. This page contains lecture notes for a couple of courses ive taught. Timpson provides the first fulllength philosophical treatment of quantum information theory and the questions it raises for our understanding of the quantum world.
Quantum information theory an overview sciencedirect topics. It is emphasized that the everyday notion of information is to be. Entropy in classical and quantum information theory. Quantum theory is a probabilistic theory, of course, and so it. Quantum information theory mathematical foundation. John watrouss lecture notes university of waterloo. Lectures on quantum information wiley online books. Quantum entanglement and information stanford encyclopedia. This idea has been applied, for example, to statistical mechanics jaynes 1957a, 1957b. The main aim of the article is to prove a theorem for quantum coding analogous to the noiseless coding theorem of shannons theory.
Adopting a block code that assigns integers to the typical sequences, the information in a string of nletters can be compressed to hx bits. It is used in the study of quantum computation and quantum cryptography. The subsections that follow present an overview of the aspects of this subject that are most relevant within the theory of quantum information. Quantum mechanics and quantum field theory by gnsecbooks. Beginning with an extensive overview of classical information theory suitable for the nonexpert, the author then turns his attention to quantum mechanics for. The quantum circuit is a basic tool of quantum information theory, so let me spend some time discussing the rules of these circuits, before going into the particulars of quantum teleportation. Quantum information theory and the foundations of quantum. In spite of these exciting developments, fundamental physics and quantum information theory remain distinct disciplines and communities, separated by signi. Wildes quantum information theory is a natural expositors labor of love. The text book for the course will be quantum computation and quantum information by m. Accessible to anyone comfortable with linear algebra and elementary probability theory, wildes book brings the reader to the forefront of research in the quantum generalization of shannons information theory.
In physics and computer science, quantum information is the information of the state of a quantum system. Finally, here is a modern, selfcontained text on quantum information theory suitable for graduatelevel courses. The general study of the information processing capabilities of quantum systems is the subject of quantum information theory. Important classes of operators the following classes of operators have particular importance in the theory of quantum information. Theory of quantum information notes from fall 2011. Information is something that can be encoded in the state of a physical system, and a computation is a task that can be performed with a physically realizable device. I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as a new physical primitivejust as, following einsteins special theory of relativity, a field is no longer regarded as the physical manifestation of. However, classics on information theory such as cover and thomas 2006 and mackay 2003 could be helpful as a reference.
Diderot all course announcements, discussion, lecture notes, lecture videos, and homework will be on diderot. In the last years, a considerable amount of theoretical and experimental studies have been focussing on the impact that quantum mechanics may have on computer science, information theory and cryptography. Quantum computation and quantum information 2018 course bulletin board. The theory of quantum information relies heavily on linear algebra in nitedimensional spaces.
Chapter 5 quantum information theory caltech particle theory. Quantum information theory is a generalization of classical information theory to use quantum mechanical particles and interference. Thats the case with quantum informationthe marriage of quantum physics and computing theory. Quantum information theory is the shannon entropy or simply entropy of the ensemble x x,px. This graduate textbook provides a unified view of quantum information theory. Quantum information theory by michael aaron nielsen. Theory of quantum information notes from fall 2011 all 22 lectures in one file lecture 1.
It is used in the study of quantum computation and quantum cryptography subcategories. Mathematical methods of quantum information theory. Quantum mechanics is the study of how microscopic physical systems change dynamically in nature. The main advances came from the mid1990s when quantum information theory developed enormously, with important work, theoretical and experimental, carried out in quantum computation, quantum.
Introduction to quantum information university of glasgow. This course will be an introduction to quantum computation and quantum information theory, from the perspective of theoretical computer science. Information quantum information processing as a distinct, widely recognized. When two good things get together, they can create something even better. Griffiths cambridge 2002 is recommended for part i of the course. John preskill with a background in highenergy physics and in computer science, my interest in quantum information was evident after the simons conference on new trends in quantum computation in 2010. Quantum information theory qita generalization of shannons classical information theory to account for the quantumphysical nature of information, information carriers, channels, and measurementsis a fast developing field, which has matured immensely over the past two decades or so. The history and future of quantum information nist. In the field of quantum information theory, the quantum systems studied are abstracted away from any real world counterpart. Its ultimate goal is to harness quantum physics to conceive and ultimately build quantum computers that would dramatically overtake the capabilities of todays classical computers. Chapter 5 quantum information theory quantum information theory is a rich subject that could easily have occupied us all term. A pair of quantum systems in an entangled state can be used as a quantum information channel to perform computational and cryptographic tasks that are impossible for classical systems. Moreover, classical information theory is formulated in the language of probability theory, so quantum information theory will be as well. This requires that understanding of basic results on diverse topics, and derived from different disciplinary perspectives, is required for appreciating the overall picture.
If you are new to information theory, then there should be enough background in this book to get you up to speed chapters 2, 10, and 14. A short introduction to quantum information and quantum computation cambridge university press, 2005. This paper seeks to provide an introduction to quantum information theory for nonphysicists at an. Quantum computation and quantum information theory course. Many di erent types of information can be accommodated within quantum mechanics, including classical information, coherent quantum information,andentanglement. Abstractions fundamental physics physics quantum information theory quantum physics theoretical physics imagine if all our scientific theories and models told us only about averages. Recent advances in quantum information theory indicate that machine learning may benefit from various paradigms of the field. The function is translated to a physical description. The goal of this course is to provide a solid understanding of the mathematical foundations of quantum information theory, with which we can then examine some of the counterintuitive phenomena in more detail. Pdf quantum information theory an invitation martin. The study of all of the above topics and differences comprises quantum information theory. Quantum information or quantum coding philsciarchive.
Chuang cambridge, 2000 in addition the book consistent quantum theory by r. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. The theory of quantum information university of waterloo. The mathematical theory of information and information processing dates to the midtwentieth century. On the other hand, pierce was quite optimistic in that he seems to have believed that. There is a feeling that the advent of quantum information theory heralds a new way of doing physics and supports the view that information should play a more central r.
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