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Information: Meanings and Interpretations

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: closed (30 June 2016) | Viewed by 28842

Special Issue Editor


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Guest Editor
Institute of Philosophy, CONICET and University of Buenos Aires, Buenos Aires 1406, Argentina
Interests: problem of the arrow of time; interpretation of quantum mechanics; nature of information; foundations of statistical mechanics; philosophy of chemistry
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Although the use of the word ‘information’, with different meanings, can be traced back to antique and medieval texts, it is only in the 20th century that the term begins to acquire its present-day connotation. Nevertheless, the pervasiveness of the notion of information, both in our everyday life and in our scientific practice, does not imply an agreement concerning the content of the concept. Nowadays, it is still a wide-ranging concept that is associated with very different phenomena, such as communication, knowledge, reference, meaning, truth, etc.

During the few last decades, new interpretive problems have arisen with the advent of quantum information, which combine the difficulties of understanding the concept of information with the well-known foundational puzzles derived from quantum mechanics itself. This situation contrasts with the huge development, in the research field, of ‘quantum information’, whereby new formal results multiply rapidly. In this context, the question of the nature of quantum information is still far from having an answer on which the whole quantum information community agrees. In fact, positions about the matter range from those who seem to deny the existence of quantum information, those who consider that it a reference to information when it is encoded in quantum systems, and those who conceive it as a new kind of information absolutely different from Shannon information.

This Special Issue aims to contribute to the discussion about the meanings and interpretations of the concept of information.

Prof. Olimpia Lombardi
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


Keywords

  • information and communication
  • classical and quantum information
  • shannon formalism
  • schumacher formalism
  • shannon entropy and von neumann entropy
  • classical and quantum coding
  • bits and qubits
  • entanglement-assisted communication
  • information in teleportation

Published Papers (5 papers)

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Research

816 KiB  
Article
Insights into Entropy as a Measure of Multivariate Variability
by Badong Chen, Jianji Wang, Haiquan Zhao and Jose C. Principe
Entropy 2016, 18(5), 196; https://doi.org/10.3390/e18050196 - 20 May 2016
Cited by 26 | Viewed by 7901
Abstract
Entropy has been widely employed as a measure of variability for problems, such as machine learning and signal processing. In this paper, we provide some new insights into the behaviors of entropy as a measure of multivariate variability. The relationships between multivariate entropy [...] Read more.
Entropy has been widely employed as a measure of variability for problems, such as machine learning and signal processing. In this paper, we provide some new insights into the behaviors of entropy as a measure of multivariate variability. The relationships between multivariate entropy (joint or total marginal) and traditional measures of multivariate variability, such as total dispersion and generalized variance, are investigated. It is shown that for the jointly Gaussian case, the joint entropy (or entropy power) is equivalent to the generalized variance, while total marginal entropy is equivalent to the geometric mean of the marginal variances and total marginal entropy power is equivalent to the total dispersion. The smoothed multivariate entropy (joint or total marginal) and the kernel density estimation (KDE)-based entropy estimator (with finite samples) are also studied, which, under certain conditions, will be approximately equivalent to the total dispersion (or a total dispersion estimator), regardless of the data distribution. Full article
(This article belongs to the Special Issue Information: Meanings and Interpretations)
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207 KiB  
Article
Information and the Quantum World
by Dennis Dieks
Entropy 2016, 18(1), 26; https://doi.org/10.3390/e18010026 - 13 Jan 2016
Cited by 5 | Viewed by 4362
Abstract
The concept of information is not different in quantum theory from its counterpart in classical physics: a sui generis quantum information concept is not needed. However, the quantum world is radically different from its classical counterpart. This difference in structure of the material [...] Read more.
The concept of information is not different in quantum theory from its counterpart in classical physics: a sui generis quantum information concept is not needed. However, the quantum world is radically different from its classical counterpart. This difference in structure of the material world has important consequences for the amounts of information that can be stored in physical systems and for the possibilities of information transfer. In many cases, overlap between quantum states (non-orthogonality of states) blurs distinctions and impedes efficient information transfer. However, the other typical quantum feature, entanglement, makes new and seemingly mysterious ways of transporting information possible. In this article, we suggest an interpretational scheme of quantum mechanics in terms of perspectival physical properties that may provide an intelligible account of these novel quantum possibilities, while staying close to the mathematical formalism of quantum mechanics. Full article
(This article belongs to the Special Issue Information: Meanings and Interpretations)
163 KiB  
Article
The Measurement Problem from the Perspective of an Information-Theoretic Interpretation of Quantum Mechanics
by Jeffrey Bub
Entropy 2015, 17(11), 7374-7386; https://doi.org/10.3390/e17117374 - 28 Oct 2015
Cited by 5 | Viewed by 6188
Abstract
The aim of this paper is to consider the consequences of an information-theoretic interpretation of quantum mechanics for the measurement problem. The motivating idea of the interpretation is that the relation between quantum mechanics and the structure of information is analogous to the [...] Read more.
The aim of this paper is to consider the consequences of an information-theoretic interpretation of quantum mechanics for the measurement problem. The motivating idea of the interpretation is that the relation between quantum mechanics and the structure of information is analogous to the relation between special relativity and the structure of space-time. Insofar as quantum mechanics deals with a class of probabilistic correlations that includes correlations structurally different from classical correlations, the theory is about the structure of information: the possibilities for representing, manipulating, and communicating information in a genuinely indeterministic quantum world in which measurement outcomes are intrinsically random are different than we thought. Part of the measurement problem is deflated as a pseudo-problem on this view, and the theory has the resources to deal with the remaining part, given certain idealizations in the treatment of macrosystems. Full article
(This article belongs to the Special Issue Information: Meanings and Interpretations)
820 KiB  
Article
Quantum Information as a Non-Kolmogorovian Generalization of Shannon’s Theory
by Federico Holik, Gustavo M. Bosyk and Guido Bellomo
Entropy 2015, 17(11), 7349-7373; https://doi.org/10.3390/e17117349 - 28 Oct 2015
Cited by 19 | Viewed by 5146
Abstract
In this article, we discuss the formal structure of a generalized information theory based on the extension of the probability calculus of Kolmogorov to a (possibly) non-commutative setting. By studying this framework, we argue that quantum information can be considered as a particular [...] Read more.
In this article, we discuss the formal structure of a generalized information theory based on the extension of the probability calculus of Kolmogorov to a (possibly) non-commutative setting. By studying this framework, we argue that quantum information can be considered as a particular case of a huge family of non-commutative extensions of its classical counterpart. In any conceivable information theory, the possibility of dealing with different kinds of information measures plays a key role. Here, we generalize a notion of state spectrum, allowing us to introduce a majorization relation and a new family of generalized entropic measures. Full article
(This article belongs to the Special Issue Information: Meanings and Interpretations)
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754 KiB  
Article
Measurement, Interpretation and Information
by Olimpia Lombardi, Sebastian Fortin and Cristian López
Entropy 2015, 17(11), 7310-7330; https://doi.org/10.3390/e17117310 - 28 Oct 2015
Cited by 6 | Viewed by 4788
Abstract
During many years since the birth of quantum mechanics, instrumentalist interpretations prevailed: the meaning of the theory was expressed in terms of measurements results. However, in the last decades, several attempts to interpret it from a realist viewpoint have been proposed. Among them, [...] Read more.
During many years since the birth of quantum mechanics, instrumentalist interpretations prevailed: the meaning of the theory was expressed in terms of measurements results. However, in the last decades, several attempts to interpret it from a realist viewpoint have been proposed. Among them, modal interpretations supply a realist non-collapse account, according to which the system always has definite properties and the quantum state represents possibilities, not actualities. But the traditional modal interpretations faced some conceptual problems when addressing imperfect measurements. The modal-Hamiltonian interpretation, on the contrary, proved to be able to supply an adequate account of the measurement problem, both in its ideal and its non-ideal versions. Moreover, in the non-ideal case, it gives a precise criterion to distinguish between reliable and non-reliable measurements. Nevertheless, that criterion depends on the particular state of the measured system, and this might be considered as a shortcoming of the proposal. In fact, one could ask for a criterion of reliability that does not depend on the features of what is measured but only on the properties of the measurement device. The aim of this article is precisely to supply such a criterion: we will adopt an informational perspective for this purpose.During many years since the birth of quantum mechanics, instrumentalistinterpretations prevailed: the meaning of the theory was expressed in terms of measurementsresults. However, in the last decades, several attempts to interpret it from a realist viewpointhave been proposed. Among them, modal interpretations supply a realist non-collapseaccount, according to which the system always has definite properties and the quantum staterepresents possibilities, not actualities. But the traditional modal interpretations faced someconceptual problems when addressing imperfect measurements. The modal-Hamiltonianinterpretation, on the contrary, proved to be able to supply an adequate account of themeasurement problem, both in its ideal and its non-ideal versions. Moreover, in the non-idealcase, it gives a precise criterion to distinguish between reliable and non-reliable measurements.Nevertheless, that criterion depends on the particular state of the measured system, and thismight be considered as a shortcoming of the proposal. In fact, one could ask for a criterionof reliability that does not depend on the features of what is measured but only on theproperties of the measurement device. The aim of this article is precisely to supply such acriterion: we will adopt an informational perspective for this purpose. Full article
(This article belongs to the Special Issue Information: Meanings and Interpretations)
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