The rapid rise of quantum information For the last four chapters I have been describing what may be called the ‘fundamental’ or ‘foundational’ aspects of quantum theory. I have been explaining what happens when you penetrate deeper into the ideas of quantum theory than when you merely make use of it, when you try to understand its basic meaning and what, if true, it tells us about the physical nature of the Universe. As I said in Chapter 5, once Bohr had given his approach to these matters in his Como paper of 1927, general opinion was that his views were sacrosanct, and that no self-respecting physicist needed to return to discuss them further. It was Bell's great achievement to dent this complacency at least a little, and from the very end of the 1960s for the next quarter of a century or so, there were a few experimentalists keen to test the Bell inequalities with increasing stringency, and a few theoreticians with fresh ideas about how quantum theory should be interpreted. While it was generally admitted that Bell's work was a genuine and important contribution to our understanding of quantum theory, and eventually the ideas actually reached some of the textbooks, in the 1970s and 1980s the field was still very much a minority interest, and even those who found it interesting would scarcely have felt that it had, or was likely to have in the foreseeable future, practical application.
The rapid rise of quantum information For the last four chapters I have been describing what may be called the ‘fundamental’ or ‘foundational’ aspects of quantum theory. I have been explaining what happens when you penetrate deeper into the ideas of quantum theory than when you merely make use of it, when you try to understand its basic meaning and what, if true, it tells us about the physical nature of the Universe. As I said in Chapter 5, once Bohr had given his approach to these matters in his Como paper of 1927, general opinion was that his views were sacrosanct, and that no self-respecting physicist needed to return to discuss them further. It was Bell's great achievement to dent this complacency at least a little, and from the very end of the 1960s for the next quarter of a century or so, there were a few experimentalists keen to test the Bell inequalities with increasing stringency, and a few theoreticians with fresh ideas about how quantum theory should be interpreted. While it was generally admitted that Bell's work was a genuine and important contribution to our understanding of quantum theory, and eventually the ideas actually reached some of the textbooks, in the 1970s and 1980s the field was still very much a minority interest, and even those who found it interesting would scarcely have felt that it had, or was likely to have in the foreseeable future, practical application.
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.
In this last chapter I shall attempt a very brief assessment of the Bohr–Einstein debate. Who won it in the view of the audience? Who actually had the better case? I will also ask two rather more specific questions. The first is ‘Have the contributions of John Bell favoured the position of either of the protagonists?’ The second is ‘Has the dramatic arrival and progress of quantum information theory anything to tell us about the Bohr–Einstein debate?’ To help to answer these questions, let me first re-assemble a few points, putting together in turn an argument for each of the protagonists against a rather hostile critic. First Bohr, and I take as his critic John Bell himself. Bell was prepared, in fact, to give Bohr great credit for what Bell called the pragmatic approach to quantum theory, which I discussed earlier. This approach says that the world must be divided into ‘classical’ and ‘quantum’ parts, with an arbitrarily placed cut between them; that the macroscopic measuring device must be described in classical terms, but that we should not expect to picture the ‘quantum’ system in physical terms, and should be content just to possess rules of calculation that work well. But Bell regarded Bohr's philosophy of what lay behind pragmatism, complementarity , as ill-defined, unsatisfactory and bizarre.
We may be on the brink of a quantum transfor -mation driven by our increasing ability to realize, detect, control, and manipulate high-purity quantum states. For decades the quantum world has crept into our lives through modern information technology, the most visible side of science that permeates almost every aspect of our daily conduct. Yet quantumness in its full glory remains a promise for the future, as existing mainstream technologies are essentially based on properties of mixed quantum states realized in, e.g., metal–oxide–semiconductor heterostructures. The scientific backbone of current technologies combines quantum theory with information theory and the theory of computation, everything being sprinkled with a healthy dose of mathematics and brought into reality by remarkable engineering achievements. This multidisciplinary approach has enabled us to understand key physical phenomena and material properties, to communicate and process information efficiently, and, ultimately, to build functional devices that provide us with unprecedented convenience and mastery over nature, possibly with the price of being in danger to become the slaves of our computers and gadgets. However, our technological success is built on a combination of essentially distinct and largely independent scientific fields. Harnessing high-purity quantum states, on the other hand, sets these previously separated “continents of knowledge” on a collision path. The main goal of the last three chapters of this book is to provide a bird's eye view of the “collision zone” and prepare the reader to explore, enjoy, and perhaps exploit the newly raising mountains. We start with a brief introduction to basic concepts in quantum information, which also includes a summary of the operational formulation of quantum mechanics (the “natural” language of quantum information theory) and a synopsis of classical information theory ( Chapter 10 ). For a thorough treatment of concepts, problems, and techniques in quantum information theory the reader is referred to the books by Nielsen and Chuang [ 389 ] and Wilde [ 548 ]. The book by Watrous [ 530 ] focuses on the mathematical theory of quantum information. An undergraduate level introduction to this subject can be found, for example, in Schumacher and Westmoreland [ 458 ]. Some of the philosophical implications of the relationship between quantum mechanics and information theory are discussed in Timpson [ 505 ]. Our survey continues with Chapter 11 , where we discuss a few key aspects pertaining to quantum computation, which can be viewed as the quintessential quantum technology involving the controlled realization and manipulation of high-purity quantum states within a large Hilbert space. Finally, Chapter 12 focuses on topological quantum computation, a promising approach to overcoming the fundamental challenge associated with quantum decoherence based on harnessing the underlying robustness of topological quantum states. This also marks our final return to the realm of topological quantum matter.
Since Bell’s death, interest in his work and quantum foundations in general, and the amount of application of his work, have grown steadily. Work on Bell’s inequality has continued, each loophole has been closed independently, and in 2015 it seems that a loophole-free test will be achieved very soon. Also stimulated by Bell, discussion of fundamental aspects of quantum theory, a discussion which was scarcely tolerated in the days of the supremacy of the Copenhagen interpretation, is widespread and productive. Bell’s work has stimulated the conception and growth of quantum information theory, which encompasses quantum computation (or quantum computing), quantum cryptography (or quantum key distribution), and quantum teleportation, and there is now an enormous amount of work, both theoretical and practical.
There are several links between information theory — between »information as such« whatever that might mean — and the foundations of nature, i e, basic physics. Well, since physics a science still evolving (despite propositions that »the end of science« now in sight), some of the links between information and physics are hypothetical. One linkage fairly obvious — thermodynamics depends upon entropy or some measure of order or disorder, and that clearly has something to do with information. The other possible relationship might be between the uncertainty that a key characteristic of quantum mechanics. We can never know everything on the quantum scale; the Heisenberg uncertainty principle tells that the more information we gain in one direction the less we know in another. If we, on that scale, obtain certainty as to one factor, then another will stay entirely undecided — try to affix a position to a quantum particle, and the momentum will be out of bounds entirely. (This the established dogma currently, though there are some deviating ideas.1) Then the question arises: who does the actual measuring, with what — what particles, at what level, are involved in this act of, as it pronounced, forcing the wave function to collapse? This wave function is the indeterminate particle: the various statistics describing the probabilities that the particle (which simultaneously takes on aspects of a wave) may be in one state or another. We will now attempt to discuss these different — or are they really different? — interdependencies, starting with black holes.