The mathematical theory of communication.

In contrast to the theories of relativity, quantum mechanics is not yet based on a generally accepted conceptual foundation. It is proposed here that the missing principle may be identified through the observation that all knowledge in physics has to be expressed in propositions and that therefore the most elementary system represents the truth value of one proposition, i.e., it carries just one bit of information. Therefore an elementary system can only give a definite result in one specific measurement. The (...) irreducible randomness in other measurements is then a necessary consequence. For composite systems entanglement results if all possible information is exhausted in specifying joint properties of the constituents. (shrink)

Whilst a straightforward consequence of the formalism of non-relativistic quantum mechanics, the phenomenon of quantum teleportation has given rise to considerable puzzlement. In this paper, the teleportation protocol is reviewed and these puzzles dispelled. It is suggested that they arise from two primary sources: (1) the familiar error of hypostatizing an abstract noun (in this case, ‘information’) and (2) failure to differentiate interpretation dependent from interpretation independent features of quantum mechanics. A subsidiary source of error, the simulation fallacy, is also (...) identified. The resolution presented of the puzzles of teleportation illustrates the benefits of paying due attention to the logical status of ‘information’ as an abstract noun. Introduction The quantum teleportation protocol 2.1 Some information-theoretic aspects of teleportation 2.1.1 Preamble 2.1.2Application to teleportation The puzzles of teleportation Resolving (dissolving) the problem 4.1 The simulation fallacy The teleportation process under different interpretations 5.1 Collapse interpretations:Dirac/von Neumann, GRW 5.2 No collapse and no extra values: Everett 5.3 No collapse, but extra values: Bohm 5.3.1 A note on active information 5.4 Ensemble and statistical viewpoints Concluding remarks. (shrink)

Recently, Brukner and Zeilinger 3354) have claimed that the Shannon information is not well defined as a measure of information in quantum mechanics, adducing arguments that seek to show that it is inextricably tied to classical notions of measurement. It is shown here that these arguments do not succeed: the Shannon information does not have problematic ties to classical concepts. In a further argument, Brukner and Zeilinger compare the Shannon information unfavourably to their preferred information measure, I , with regard (...) to the definition of a notion of “total information content.” This argument is found unconvincing and the relationship between individual measures of information and notions of “total information content” investigated. We close by considering the prospects of Zeilinger's Foundational Principle as a foundational principle for quantum mechanics. (shrink)

Through a study of a sophisticated contemporary scientific experiment, it is shown how and why use of the term 'observation' in reference to that experiment departs from ordinary and philosophical usages which associate observation epistemically with perception. The role of "background information" is examined, and general conclusions are arrived at regarding the use of descriptive language in and in talking about science. These conclusions bring out the reasoning by which science builds on what it has learned, and, further, how that (...) process of building consists not only in adding to our substantive knowledge, but also in increasing our ability to learn about nature, by extending our ability to observe it in new ways. The argument of this paper is thus a step toward understanding how it is that all our knowledge of nature rests on observation. (shrink)

Some physicists seem to believe that quantum information theory requires a new concept of information (Jozsa, 1998, Quantum information and its properties. In: Hoi-Kwong Lo, S. Popescu, T. Spiller (Eds.), Introduction to Quantum Computation and Information, World Scientific, Singapore, (pp. 49-75); Deutsch & Hayden, 1999, Information flow in entangled quantum subsystems, preprint quant-ph/9906007). I will argue that no new concept is necessary. Shannon's concept of information is sufficient for quantum information theory. Properties that are cited to contrast quantum information and (...) classical information (i.e., Shannon information) actually point to differences in our ability to manipulate, access, and transfer information depending on whether quantum systems, opposed to classical systems, are used in a communication system. I also demonstrate that conceptually puzzling phenomena in quantum information theory, such as dense coding, teleportation, and Schumacher coding, all of which are cited as evidence that a new concept of information is required, do not have to be regarded as such. (shrink)

We consider probabilistic theories in which the most elementary system, a two-dimensional system, contains one bit of information. The bit is assumed to be contained in any complete set of mutually complementary measurements. The requirement of invariance of the information under a continuous change of the set of mutually complementary measurements uniquely singles out a measure of information, which is quadratic in probabilities. The assumption which gives the same scaling of the number of degrees of freedom with the dimension as (...) in quantum theory follows essentially from the assumption that all physical states of a higher dimensional system are those and only those from which one can post-select physical states of two-dimensional systems. The requirement that no more than one bit of information (as quantified by the quadratic measure) is contained in all possible post-selected two-dimensional systems is equivalent to the positivity of density operator in quantum theory. (shrink)

This book develops an explanation for the roles of observation and theory in scientific endeavor that occupies the middle ground between empiricism and rationalism, and captures the strengths of both approaches. Brown argues that philosophical theories have the same epistemological status as scientific theories and constructs an epistemological theory that provides an account of the role that theory and instruments play in scientific observation. His theory of perception yields a new analysis of objectivity that combines the traditional view of observation (...) as the foundation of scientific objectivity with the contemporary recognition that observation is theory-dependent. (shrink)

This book helps us understand the true meaning of the concept and how it can be used to understand our world.

Christopher G. Timpson provides the first full-length philosophical treatment of quantum information theory and the questions it raises for our understanding of the quantum world. He argues for an ontologically deflationary account of the nature of quantum information, which is grounded in a revisionary analysis of the concepts of information.

The concept of observability of entities in physical science is typically analyzed in terms of the nature and significance of a dichotomy between observables and unobservables. In the present work, however, this categorization is resisted and observability is analyzed in a descriptive way in terms of the information which one can receive through interaction with objects in the world. The account of interaction and the transfer of information is done using applicable scientific theories. In this way, the question of observability (...) of scientific entities is put to science itself. ;Several examples are presented which show how this interaction-information account of observability is done. It is demonstrated that observability has many dimensions which are, in general, orthogonal. The epistemic significance of these dimensions is explained. ;This study is intended primarily as a method for understanding problems of observability rather than as a solution to those problems. The important issue of scientific realism and its relation to observability, however, demand attention. Hence, the implication of the interaction-information account for realism, and the implication of realism for the interaction-information account of observability are discussed in the end. (shrink)