Quantum information theory

[摘要] 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 definitemeaning. What is information, and how would one process it? It took the development oftheories of computing (in the 1930s) and information (late in the 1940s) for us to formulatemathematically what it means to compute or communicate.Yet these theories were abstract, based on axiomatic mathematics: what did physical systemshave to do with these axioms? Rolf Landauer had the essential insight - Information isphysical - that information is always encoded in the state of a physical system, whose dynamicson a microscopic level are well-described by quantum physics. This means that we cannot discussinformation 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 unreasonableeffectiveness of mathematics in the natural sciences. Why are the computational techniquesof mathematics so astonishingly useful in describing the physical world [1]? One might begin tosuspect 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 particularyear in which an explosion of interest took place in information physics, that year would have tobe 1994, when Shor showed that a problem of practical interest (factorisation of integers) could besolved easily on a quantum computer. But the applications of information in physics - and viceversa - have been far more widespread than this popular discovery. These applications rangefrom improved experimental technology, more sophisticated measurement techniques, methodsfor characterising the quantum/classical boundary, tools for quantum chaos, and deeper insightinto quantum theory and nature.In this thesis I present a short review of ideas in quantum information theory. The first chaptercontains introductory material, sketching the central ideas of probability and information theory.Quantum mechanics is presented at the level of advanced undergraduate knowledge, together withsome useful tools for quantum mechanics of open systems. In the second chapter I outline howclassical information is represented in quantum systems and what this means for agents tryingto extract information from these systems. The final chapter presents a new resource: quantuminformation. This resource has some bewildering applications which have been discovered in thelast ten years, and continually presents us with unexpected insights into quantum theory andthe universe.

[发布机构] Stellenbosch University