What are the information processing capabilities of physical systems?As recently as the first half of the 20 th century this question did not even have a definite meaning.What is information, and how would one process it?It took the development of theories of computing (in the 1930s) and information (late in the 1940s) for us to formulate mathematically what it means to compute or communicate.Yet these theories were abstract, based on axiomatic mathematics: what did physical systems have to do with these axioms?Rolf Landauer had the essential insight -"Information is physical" -that information is always encoded in the state of a physical system, whose dynamics on a microscopic level are well-described by quantum physics.This means that we cannot discuss information without discussing how it is represented, and how nature dictates it should behave.Wigner considered the situation from another perspective when he wrote about "the unreasonable effectiveness of mathematics in the natural sciences".Why are the computational techniques of mathematics so astonishingly useful in describing the physical world [1]?One might begin to suspect foul play in the universe's operating principles.Interesting insights into the physics of information accumulated through the 1970s and 1980s -most sensationally in the proposal for a "quantum computer".If we were to mark a particular year in which an explosion of interest took place in information physics, that year would have to be 1994, when Shor showed that a problem of practical interest (factorisation of integers) could be solved easily on a quantum computer.But the applications of information in physics -and vice versa -have been far more widespread than this popular discovery.These applications range from improved experimental technology, more sophisticated measurement techniques, methods for characterising the quantum/classical boundary, tools for quantum chaos, and deeper insight into quantum theory and nature.In this thesis I present a short review of ideas in quantum information theory.The first chapter contains introductory material, sketching the central ideas of probability and information theory.Quantum mechanics is presented at the level of advanced undergraduate knowledge, together with some useful tools for quantum mechanics of open systems.In the second chapter I outline how classical information is represented in quantum systems and what this means for agents trying to extract information from these systems.The final chapter presents a new resource: quantum information.This resource has some bewildering applications which have been discovered in the last ten years, and continually presents us with unexpected insights into quantum theory and the universe.ii This thesis is dedicated to my mother.iii This thesis was begun as an intrepid adventure.It caught
What are the information processing capabilities of physical systems?As recently as the first half of the 20 th century this question did not even have a definite meaning.What is information, and how would one process it?It took the development of theories of computing (in the 1930s) and information (late in the 1940s) for us to formulate mathematically what it means to compute or communicate.Yet these theories were abstract, based on axiomatic mathematics: what did physical systems have to do with these axioms?Rolf Landauer had the essential insight -"Information is physical" -that information is always encoded in the state of a physical system, whose dynamics on a microscopic level are well-described by quantum physics.This means that we cannot discuss information without discussing how it is represented, and how nature dictates it should behave.Wigner considered the situation from another perspective when he wrote about "the unreasonable effectiveness of mathematics in the natural sciences".Why are the computational techniques of mathematics so astonishingly useful in describing the physical world [1]?One might begin to suspect foul play in the universe's operating principles.Interesting insights into the physics of information accumulated through the 1970s and 1980s -most sensationally in the proposal for a "quantum computer".If we were to mark a particular year in which an explosion of interest took place in information physics, that year would have to be 1994, when Shor showed that a problem of practical interest (factorisation of integers) could be solved easily on a quantum computer.But the applications of information in physics -and vice versa -have been far more widespread than this popular discovery.These applications range from improved experimental technology, more sophisticated measurement techniques, methods for characterising the quantum/classical boundary, tools for quantum chaos, and deeper insight into quantum theory and nature.In this thesis I present a short review of ideas in quantum information theory.The first chapter contains introductory material, sketching the central ideas of probability and information theory.Quantum mechanics is presented at the level of advanced undergraduate knowledge, together with some useful tools for quantum mechanics of open systems.In the second chapter I outline how classical information is represented in quantum systems and what this means for agents trying to extract information from these systems.The final chapter presents a new resource: quantum information.This resource has some bewildering applications which have been discovered in the last ten years, and continually presents us with unexpected insights into quantum theory and the universe.ii This thesis is dedicated to my mother.iii This thesis was begun as an intrepid adventure.It caught
ENGLISH ABSTRACT: What are the information processing capabilities of physical systems? As recently as the first half of the 20th century this question did not even have a definite meaning. What is information, and how would one process it? It took the development of theories of computing (in the 1930s) and information (late in the 1940s) for us to formulate mathematically what it means to compute or communicate. Yet these theories were abstract, based on axiomatic mathematics: what did physical systems have to do with these axioms? Rolf Landauer had the essential insight - "Information is physical" - that information is always encoded in the state of a physical system, whose dynamics on a microscopic level are well-described by quantum physics. This means that we cannot discuss information without discussing how it is represented, and how nature dictates it should behave. Wigner considered the situation from another perspective when he wrote about "the unreasonable effectiveness of mathematics in the natural sciences". Why are the computational techniques of mathematics so astonishingly useful in describing the physical world [1]? One might begin to suspect foul play in the universe's operating principles. Interesting insights into the physics of information accumulated through the 1970s and 1980s - most sensationally in the proposal for a "quantum computer". If we were to mark a particular year in which an explosion of interest took place in information physics, that year would have to be 1994, when Shor showed that a problem of practical interest (factorisation of integers) could be solved easily on a quantum computer. But the applications of information in physics - and vice versa - have been far more widespread than this popular discovery. These applications range from improved experimental technology, more sophisticated measurement techniques, methods for characterising the quantum/classical boundary, tools for quantum chaos, and deeper insight into quantum theory and nature. In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level of advanced undergraduate knowledge, together with some useful tools for quantum mechanics of open systems. In the second chapter I outline how classical information is represented in quantum systems and what this means for agents trying to extract information from these systems. The final chapter presents a new resource: quantum information. This resource has some bewildering applications which have been discovered in the last ten years, and continually presents us with unexpected insights into quantum theory and the universe.
The theoretical, experimental and technological areas covering the use of quantum mechanics for communication and computation.Quantum information processing includes investigations in quantum information theory, quantum communication, quantum computation, quantum algorithms and their complexity, and quantum control.The science of quantum information processing is a highly interdisciplinary field.In the context of mathematics it is stimulating research in pure mathematics (e.g.coding theory, *algebras, quantum topology) as well as requiring and providing many opportunities for applied mathematics.The science of quantum information processing emerged from the recognition that usable notions of information need to be physically implementable.In the 1960s and 1970s researchers such as R. Landauer, C. Bennett, C. Helstrom and A. Holevo realized that the laws of physics give rise to fundamental constraints on the ability to implement and manipulate information.Landauer repeatedly stated that "information is physical", providing impetus to the idea that it should be possible to found theories of information on the laws of physics.This is in contrast to the introspective approach which led to the basic definitions of computer science and information theory as formulated by A. Church, A. Turing, C. Shannon and others in the first half of the 20th century.Early work in studying the physical foundations of information focused on the effects of energy limitations and the need for dissipating heat in computation and communication.Beginning with S. Wiesner's work on applications of quantum mechanics to cryptography in the late 1960s, it was realized that there may be intrinsic advantages to using quantum physics in information processing.Quantum cryptography and quantum communication in general were soon established as interesting and non-trivial extensions of classical communication based on bits.That quantum mechanics may be used to improve the efficiency of algorithms was first realized when attempts at simulating quantum mechanical systems resulted in exponentially complex algorithms compared to the physical resources associated with the system simulated.In the 1980s, P. Benioff and R. Feynman introduced the idea of a quantum computer for efficiently implementing quantum physics simulations.Models of quantum computers were developed by D. Deutsch, leading to the formulation of artificial problems that could be solved more efficiently by quantum than by classical computers.The advantages of quantum computers became widely recognized when P.
In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level of advanced undergraduate knowledge, together with some useful tools for quantum mechanics of open systems. In the second chapter I outline how classical information is represented in quantum systems and what this means for agents trying to extract information from these systems. The final chapter presents a new resource: quantum information. This resource has some bewildering applications which have been discovered in the last ten years, and continually presents us with unexpected insights into quantum theory and the universe. The treatment is pedagogical and suitable for beginning graduates in the field.
Quantum information theory represents a rich subject of discussion for those interested in the philosphical and foundational issues surrounding quantum mechanics for a simple reason: one can cast its central concerns in terms of a long-familiar question: How does the quantum world differ from the classical one? Moreover, deployment of the concepts of information and computation in novel contexts hints at new (or better) means of understanding quantum mechanics, and perhaps even invites re-assessment of traditional material conceptions of the basic nature of the physical world. In this paper I review some of these philosophical aspects of quantum information theory, begining with an elementary survey of the theory, seeking to highlight some of the principles and heuristics involved. We move on to a discussion of the nature and definition of quantum information and deploy the findings in discussing the puzzles surrounding teleportation. The final two sections discuss, respectively, what one might learn from the development of quantum computation (both about the nature of quantum systems and about the nature of computation) and consider the impact of quantum information theory on the traditional foundational questions of quantum mechanics (treating of the views of Zeilinger, Bub and Fuchs, amongst others).
Quantum information theory represents a rich subject of discussion for those interested in the philosphical and foundational issues surrounding quantum mechanics for a simple reason: one can cast its central concerns in terms of a long-familiar question: How does the quantum world differ from the classical one? Moreover, deployment of the concepts of information and computation in novel contexts hints at new (or better) means of understanding quantum mechanics, and perhaps even invites re-assessment of traditional material conceptions of the basic nature of the physical world. In this paper I review some of these philosophical aspects of quantum information theory, begining with an elementary survey of the theory, seeking to highlight some of the principles and heuristics involved. We move on to a discussion of the nature and definition of quantum information and deploy the findings in discussing the puzzles surrounding teleportation. The final two sections discuss, respectively, what one might learn from the development of quantum computation (both about the nature of quantum systems and about the nature of computation) and consider the impact of quantum information theory on the traditional foundational questions of quantum mechanics (treating of the views of Zeilinger, Bub and Fuchs, amongst others).
Quantum Information Science is a cross-disciplinary subject that has arisen in the last twenty years. It concerns itself with the consequences of our most complete description of the physical world (that is, quantum mechanics) for the reliable, secure, private, and rapid processing of information, both in communication and computation. While its invention is often ascribed to the famous theoretical physicist Richard Feynman in the 1980s, his contributions were only one of many that initiated the field around that time. While he perceived that new types of physical devices, in which the quantum laws of superposition and entanglement function at the logical level, could give new power in the simulation of quantum physics, it was others (Bennett, Brassard) who showed that the uncertainty principle led to fundamentally more secure ways of communicating secret messages. It was yet others (Deutsch, Vazirani) who understood that quantum theory defined a new kind of Turing machine, and that not only quantum physics simulations, but potentially many other computational problems, are sped up in this machine. And it was yet another (Shor) who found a simple, very fast algorithm for prime factorization. The word "qubit" was coined only in 1995. Its introduction is indicative of a new mindset that has developed in recent years for studying and using quantum systems. "Qubit" now stands for a durable paradigm that spans a very wide variety of fields. It thus has many sub-meanings: first, it is the basic abstract unit of information for workers ranging from optical communication engineers to NMR spectroscopists to black-hole theorists. Second, it is the name we now routinely give to physical two level systems, as they are realized by photons, atomic and ionic eigenlevels, electronic and nuclear spin, structural defects in solids, and circulating-current states of superconducting devices. Physics has long dealt with some of these two-level systems, but calling them qubits implies a whole suite of interrelated ideas and capabilities that we ascribe to these systems: the ability to precisely set, and to precisely measure, the quantum state of one unique specimen, to avoid its coupling with the environment while at the same time strongly and controllably coupling the qubits together, to exploit the resulting quantum entanglement as a resource for metrological, cryptographic, and computational tasks. Quantum Information is a very diverse subject pursued today in many different directions, by many hundreds of researchers internationally: In theoretical physics, it has enlivened and sharpened the understanding of efficient representations of entangled many-particle wavefunctions, and has provided the prospect of applications for new concepts such as anyons and majorana fermions. Information theorists has benefitted from having a rigorous extension of the basis of their field, in which classical information theory is subsumed into a greatly broader subject. Theoretical computer scientists continue the search for new quantum algorithms, and have used quantum concepts to prove new results about the classification of computational complexity. Coding theorists have had the new and subtle problem of quantum error correction to analyse and conquer. Most strikingly, the program of experimental physics has been influenced in many directions by Quantum Information Science. State-of-the-art optics experiments transmit quantum states over long distances and perform precision manipulations in single quanta (atomic ions, impurity spins, quantum dots) in the quest to have working quantum cyptography and quantum computing. Quantum Hall systems, and topological insulators, are being assiduously examined for new elementary excitations for use as qubits. In the course of ten years, superconducting devices have improved by over four orders of magnitude in their quantum coherence, a metric made precise by the ideas of quantum computing. [...] DiVincenzo, David