Shannon considered only classical physics without quantum e ects his work and that of others ultimately led to questions like. Chapter 1 describes an algebraic technique which extends several previously known qubit channel capacity results to the qudit quantum channel case. Emergence of classical reality from within quantum theory oral thesis presentation david poulin institute for quantum computing perimeter institute. The solutions on this website do not print correctly, although they can be viewed properly, when using current versions of internet explorer. First, there is a good motivation for controlling quantum systems. 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. A particle follows the usual rules of quantum theory. The work, quantum information theory, 2nd edition is to be published. As such, we spend a significant amount of time on quantum mechanics for quantum information theory part ii, we give a careful study of.
Additivity in classical and quantum information theory. The fundamental basis of quantum computation is landauers observation that all information is ultimately physical 1, 2. There is substantial interest in extending the concepts from classical control theory to settings governed by quantum mechanics. Wilde, from classical to quantum shannon theory 2016, pdf at arxiv. Vyalyi american mathematical society providence, rhode island. Quantum information theory by michael aaron nielsen. Request pdf classical and quantum information a new discipline, quantum information science, has emerged in the last two decades of the twentieth century at the intersection of physics.
Quantum mechanics, concepts and applications, by n. The conception of quantum information was introduced in the theory of quantum information studying the phenomena of entanglement in quantum mechanics the entanglement was theoretically forecast in the famous papers of einstein, podolsky, and rosen 1935 and independently by shrodinger 1935 deducing it from hilbert space, the basic. At its heart quantum mechanics is a mathemat ically abstract subject expressed in terms of the language of complex linear vector spaces in other words, linear algebra. But since mathematics is the language of nature, its required to quantify the prediction of quantum mechanics. Quantum information theory is the shannon entropy or simply entropy of the ensemble x x,px. The subsections that follow present an overview of the aspects of this subject that are most relevant within the theory of quantum information. Transition from classical physics to quantum mechanics. Lecture notes on quantum information and computation yong zhang1 school of physics and technology, wuhan university fall 2015 abstract these lectures notes are written for both advanced undergraduate students and rstyear graduate students in the school of physics and technology, university wuhan. Beyond that, quantum mechanics is needed to explain radioactivity, how semiconducting. The audience consisted of advanced undergraduates and beginning graduate students.
Classical information theory characterizes the channel resources required for the transmission of classical data, asymptotically reliable transmission being possible if and only if the channel capacity exceeds the source entropy there is also a welldeveloped theory of the optimum use of quantum channels to carry classical information. Information theory lies at the heart of modern technology, underpinning all communications, networking, and data storage systems. In the second part, we develop a framework of semide. The aim of this book is to develop from the ground up many of the major, exciting, pre and postmillenium developments in the general area of study known as quantum shannon theory. From classical to quantum shannon theory inspire hep. Quantum information theory exploded in 1994 when peter shor published his algorithm that can break rsa encryption codes. Bennett and peter shor 52 pages this is a survey on quantum information theory which will appear in the ieee transactions on information theory october, 1998. Wesley weiherdammstrasse 24 78176 blumberg, germany from the extensive observations and the ideas of newton and from classical physical optics the velocity of a quantum particle is given by w s e, where. Classical mechanics is about movement and change, while the strong emphasis on stationary states in traditional quantum courses makes the quantum world seem static and irreconcilably di. The course gives an introduction into classical and quantum computing. For instance, suppose we would like to transmit a given source of data e. Request pdf classical and quantum information a new discipline, quantum information science, has emerged in the last two decades of the twentieth century at. Vyalyi american mathematical society providence, rhode island graduate studies in mathematics. 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.
An introduction to control theory from classical to. Throughout, the reader is introduced to key results without becoming lost in mathematical details. Ssa quantum mechanics quantum information pdf strong subadditivity of entropy ssa was long known and appreciated in classical probability theory and information theory. Wesley weiherdammstrasse 24 78176 blumberg, germany from the extensive observations and the ideas of newton and from classical physical optics the velocity of a quantum particle is given by w s e, where s is the poynting vector and e the wave energy density. A few years later, he published an algorithm in 1985 that was the rst instance. Quantum control is particularly exciting because it satis. The second part includes the descriptions of basic e. Quantum information differs strongly from classical information, epitomized by the bit, in many striking and unfamiliar ways.
To describe the quantum properties of any physical system, a new mathematical language is re quired as compared to that of classical mechanics. Wilde hearne institute for theoretical physics department of physics and astronomy center for computation and technology louisiana state university baton rouge, louisiana 70803, usa arxiv. A certain level of familiarity with general relativity and quantum mechanics is required, although many of the necessary results are derived in the text. In retrospect, this development seems somewhat belated, since quantum mechanics has long been thought to underlie. Review of the book classical and quantum information theory. Classical and quantum information theory an introduction for the telecom scientist information theory lies at the heart of modern technology, underpinning all communications, networking, and data storage systems. An introduction to control theory from classical to quantum. Another great book is the book by kitaev, shen and vialyi, classical and quantum computation. This book sets out, for the first time, a complete overview of both classical and quantum information theory. Quantum information theory postscript postscript or pdf, by charles h. Information content decodable data in terms of 0s and 1s into meaningful characters the processing of information quantum or classical computation methodological comparisons in measuring information.
Introduction to quantum information theoryphys 7895 this course introduces the subject of communication with quantum systems. An introduction for the telecom scientist emmanuel desurvire download bok. Could have been more, since there are more classical inequalities. Exploring the rich variety of capabilities allowed by these types of information is the subject of quantum information theory, and of this dissertation. Deutsch claims that he could immediately see that the quantum theory would give an im. Emergence of classical reality from within quantum theory oral thesis presentation david poulin institute for quantum computing perimeter institute for theoretical physics waterloo, november 2004 p. As such, we spend a significant amount of time on quantum mechanics for quantum information theory part ii, we give a careful study of the important. Emergence of classical reality from within quantum theory. A classicalquantum coincidence we can do this whole game for classical entropy formulas too. Lecture notes on quantum information and computation. Qit is the study of how these tasks can be accomplished, using quantum mechanical systems.
For those of you interested in quantum information theory, the book by mark wilde, from classical to quantum shannon theory, is a great res ource, and it is also available online. 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. Chuang, quantum computation and quantum information, cambridge university press 2000 mark m. As such, we spend a significant amount of time on quantum mechanics for quantum information theory part ii, we give a careful study of the important unit. Classical and quantum information marinescu, dan c. The work, quantum information theory, 2nd edition is to be published by cambridge. Quantum information theory and the foundations of quantum. Claude shannon established the two core results of classical information theory in his landmark 1948 paper. In particular, i demonstrate several novel limits to the information processing ability of quantum. A short introduction to quantum information and quantum computation cambridge university press, 2005. I learned early on in my undergraduate education that while it is instructive to read, and to attend to the words of informed speakers, i cannot gain the feeling that i understand a subject until i have done my best to write about it.
Review of the book classical and quantum information. In some cases quantum algorithms can be used to perform computations faster than in any known classical algorithm. In the topic along with closely related questions in. The wave function of a quantum system is a vector f in a hilbert space h, comprising possible wave functions. While the fundamental unit of classical information is the bit, the most basic unit of quantum information is the qubit. Quantum information theory qit lies at the intersection of mathematics, physics and computer science. In this sense a letter xchosen from the ensemble carries, on the average, hx bits of information. A fewbut only a fewof those notebooks are reproduced here. This graduate textbook provides a unified view of quantum information theory. Coding theorems of classical and quantum information theory k.
A short course in quantum information theory springer, 2007. Classical and quantum computing university of johannesburg. A classical quantum coincidence we can do this whole game for classical entropy formulas too. But uniform additivity only uses strong subadditivity. Parthasarathy and others published coding theorems of classical and quantum information theory find, read and cite. Adopting a block code that assigns integers to the typical sequences, the information in a string of nletters can be compressed to hx bits. Methodological comparisons in measuring information. Additivity in classical and quantum information theory andrew cross, ke li, graeme smith ibm tj watson research center, kl also with center for theoretical physics, mit. We deal concretely with some concepts that appear in more abstract form in later chapters. Chapter 2 derives a formula for the relative entropy function of two qubit density matrices in terms of their bloch vectors. Pdf from classical to quantum shannon theory researchgate. Important classes of operators the following classes of operators have particular importance in the theory of quantum information.
Qit is the study of how these tasks can be accomplished, using quantummechanical systems. An introduction to quantum physics by french and talyor. Coding theorems of classical and quantum information theory. We shall loosely refer to this vast and variegated field as quantum information 71, 48, 100, 128, 224, 242, 152, 239, 307. Classical and quantum information theory springerlink.
Classically, information is encoded in a sequence of bits, i. Some remarks concerning the origins and nature of this material. It is assumed that the reader is already familiar with the most. Figure 1 is just one example of a huge variety of quantum circuits that are used to compactly. The old ssa theorem on quantum entropy played an important role and i began to. Quantum information theory exercise sheet 6 exercise 6.
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