A classical quantum coincidence we can do this whole game for classical entropy formulas too. The wave function of a quantum system is a vector f in a hilbert space h, comprising possible wave functions. To describe the quantum properties of any physical system, a new mathematical language is re quired as compared to that of classical mechanics. Review of the book classical and quantum information theory. It was born out of classical information theory, which is the mathematical theory of acquisition, storage, transmission and processing of information. Parthasarathy and others published coding theorems of classical and quantum information theory find, read and cite. 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. Chapter 1 describes an algebraic technique which extends several previously known qubit channel capacity results to the qudit quantum channel case. Classical and quantum computing university of johannesburg. 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.
The purpose of this chapter is to provide an overview of quantum information theory starting from classical information theory, with the aim to. But uniform additivity only uses strong subadditivity. Shannon considered only classical physics without quantum e ects his work and that of others ultimately led to questions like. A few years later, he published an algorithm in 1985 that was the rst instance. In the topic along with closely related questions in. Clearly explaining the necessary mathematical basis, it merges key topics from both information theoretic and quantum mechanical viewpoints and provides lucid explanations of the basic results. In some cases quantum algorithms can be used to perform computations faster than in any known classical algorithm. The fundamental basis of quantum computation is landauers observation that all information is ultimately physical 1, 2. Some remarks concerning the origins and nature of this material. A fewbut only a fewof those notebooks are reproduced here. In particular, i demonstrate several novel limits to the information processing ability of quantum. Beyond that, quantum mechanics is needed to explain radioactivity, how semiconducting. The work, quantum information theory, 2nd edition is to be published by cambridge. 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.
Could have been more, since there are more classical inequalities. 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 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. Deutsch claims that he could immediately see that the quantum theory would give an im. Chuang, quantum computation and quantum information, cambridge university press 2000 mark m. 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.
Vyalyi american mathematical society providence, rhode island graduate studies in mathematics. Exploring the rich variety of capabilities allowed by these types of information is the subject of quantum information theory, and of this dissertation. Quantum mechanics, concepts and applications, by n. Quantum information theory is the shannon entropy or simply entropy of the ensemble x x,px. In this sense a letter xchosen from the ensemble carries, on the average, hx bits of information.
Ssa quantum mechanics quantum information pdf strong subadditivity of entropy ssa was long known and appreciated in classical probability theory and information theory. We shall loosely refer to this vast and variegated field as quantum information 71, 48, 100, 128, 224, 242, 152, 239, 307. 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. Vyalyi american mathematical society providence, rhode island. Coding theorems of classical and quantum information theory. Emergence of classical reality from within quantum theory.
In the second part, we develop a framework of semide. Classical information is measured using shannon entropy, while the quantum mechanical. Additivity in classical and quantum information theory. Classical and quantum information marinescu, dan c. A certain level of familiarity with general relativity and quantum mechanics is required, although many of the necessary results are derived in the text. Quantum information differs strongly from classical information, epitomized by the bit, in many striking and unfamiliar ways. An introduction for the telecom scientist emmanuel desurvire download bok. 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. Although quantum shannon theory is the oldest part of. Quantum information theory qit lies at the intersection of mathematics, physics and computer science. Qit is the study of how these tasks can be accomplished, using quantum mechanical systems.
An introduction to quantum physics by french and talyor. The old ssa theorem on quantum entropy played an important role and i began to. 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. The solutions on this website do not print correctly, although they can be viewed properly, when using current versions of internet explorer.
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. Classical and quantum information theory springerlink. But since mathematics is the language of nature, its required to quantify the prediction of quantum mechanics. Pdf from classical to quantum shannon theory researchgate. The work, quantum information theory, 2nd edition is to be published. 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. The course gives an introduction into classical and quantum computing. A short course in quantum information theory springer, 2007. Review of the book classical and quantum information.
Introduction to quantum information theoryphys 7895 this course introduces the subject of communication with quantum systems. While the fundamental unit of classical information is the bit, the most basic unit of quantum information is the qubit. Figure 1 is just one example of a huge variety of quantum circuits that are used to compactly. 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. 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. Quantum information theory by michael aaron nielsen. Classical and quantum information theory by emmanuel desurvire cambridge univ. Throughout, the reader is introduced to key results without becoming lost in mathematical details. Qit is the study of how these tasks can be accomplished, using quantummechanical systems. There is substantial interest in extending the concepts from classical control theory to settings governed by quantum mechanics.
Classically, information is encoded in a sequence of bits, i. First, there is a good motivation for controlling quantum systems. We deal concretely with some concepts that appear in more abstract form in later chapters. 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. Another great book is the book by kitaev, shen and vialyi, classical and quantum computation. Quantum information theory exploded in 1994 when peter shor published his algorithm that can break rsa encryption codes.
An introduction to control theory from classical to. From classical to quantum shannon theory inspire hep. 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. This graduate textbook provides a unified view of quantum information theory. Quantum control is particularly exciting because it satis. 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. Important classes of operators the following classes of operators have particular importance in the theory of quantum information. Information, the 1s and 0s of classical computers, must inevitably be recorded by some physical system be it paper or silicon. Coding theorems of classical and quantum information theory k.
A short introduction to quantum information and quantum computation cambridge university press, 2005. Claude shannon established the two core results of classical information theory in his landmark 1948 paper. For instance, suppose we would like to transmit a given source of data e. This book sets out, for the first time, a complete overview of both classical and quantum information 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.
Lecture notes on quantum information and computation. 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. Methodological comparisons in measuring information. An introduction to control theory from classical to quantum. Quantum information theory exercise sheet 6 exercise 6. The theory of quantum information relies heavily on linear algebra in nitedimensional spaces. In retrospect, this development seems somewhat belated, since quantum mechanics has long been thought to underlie.
Information theory lies at the heart of modern technology, underpinning all communications, networking, and data storage systems. The subsections that follow present an overview of the aspects of this subject that are most relevant within the theory of quantum information. A classicalquantum coincidence we can do this whole game for classical entropy formulas too. 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. It is assumed that the reader is already familiar with the most. 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. Request pdf classical and quantum information a new discipline, quantum information science, has emerged in the last two decades of the twentieth century at.
Quantum information theory postscript postscript or pdf, by charles h. This thesis studies classical communication over quantum channels. Wilde, from classical to quantum shannon theory 2016, pdf at arxiv. Transition from classical physics to quantum mechanics. Emergence of classical reality from within quantum theory oral thesis presentation david poulin institute for quantum computing perimeter institute. Quantum information theory and the foundations of quantum. The audience consisted of advanced undergraduates and beginning graduate students. Chapter 2 derives a formula for the relative entropy function of two qubit density matrices in terms of their bloch vectors. 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. 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. As such, we spend a significant amount of time on quantum mechanics for quantum information theory part ii, we give a careful study of. 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. The second part includes the descriptions of basic e. A particle follows the usual rules of quantum theory.
843 447 904 948 151 748 1488 1382 901 1535 391 955 29 1229 1324 1464 1222 1279 350 1524 66 1050 805 931 864 413 125 1297 169 1341 148 623 980 88 883 1085 1065 316 70 331