By analogy with the Industrial Revolution, at present many people talk about an Information Revolution that began in the mid-twentieth century and continues to this day. Although triggered by the advent of digital technologies and established by the proliferation of digital computers, the drastic changes rapidly exceeded the limits of technology to pervade all aspects of social life. Nowadays, information shapes all our everyday activities and thoughts.
Given this situation, it is not surprising that, during the past decades, philosophy has begun to focus its attention on the search of an elucidation of the notion of information. The many dimensions of information make this task particularly interesting from a philosophical viewpoint, but, at the same time, attempt against a unified answer to the problem. At present, different interpretations of the notion of information coexist, sometimes as the consequence of implicitly conflating its different meanings, but in many cases also as the result of the multiple facets of the concept.
At the same time, new interpretive problems have arisen with the advent of the research field called “quantum information theory.” Those problems combine the difficulties in the understanding of the concept of information with the well-known foundational puzzles derived from quantum mechanics itself. Of course, interpretive issues were not an obstacle to the huge development of quantum information theory as a scientific area of research, where new formal results multiply rapidly. Nevertheless, the question “What is quantum information?” is still far from having an answer on which the whole quantum information community agrees.
It is in this context that the question about the nature of quantum information deserves to be considered from a conceptual viewpoint. The aim of this volume is, precisely, to address the issue from several and varied perspectives, which makes manifest its different aspects and its many implications. With this purpose, the chapters of this volume are organized in three parts. Part I, “The Concept of Information,” groups the chapters mainly devoted to inquiring into the concept itself and its relationships with other notions, such as knowledge, representation, and manipulation. In Part II, “Information and Quantum Mechanics,” the links between informational and quantum issues enter the stage. Finally, Part III, “Probability, Correlations, and Information,” addresses the subject matter by considering how the notions of probability and correlation underlie the concept of information in different problem domains.
Part I opens with the chapter “About the Concept of Information,” where Sebastian Fortin and Olimpia Lombardi begin by introducing some relevant distinctions that allow them to focus on mathematical information in the communicational context. In this context, after discussing the definition of some magnitudes involved in the Shannon formalism, the chapter deals entirely with interpretive matters. First, three interpretations of the concept of information are introduced, stressing their differences and specific difficulties. Then, the question about the existence of two qualitatively different kinds of information, classical and quantum, is addressed. On the basis of the previous discussion, the authors advocate for a theoretically neutral interpretation of information.
The main aim of the second chapter of this first part, “Representation, Interpretation, and Theories of Information,” by Armond Duwell, is to stress the vital importance of representational and interpretive aspects for understanding the definition of information provided by Christopher Timpson. With this purpose, the chapter begins with discussing some basic features of representation and interpretation of theories. Then, two potential problems of Timpson’s definition in Shannon information theory and in quantum information theory, respectively, are considered; the argumentation is directed to show that the resolution to those problems depends on recognizing how important users of the information theories are in determining what constitutes successful quantum information transfer. On this basis, the author concludes that Timpson’s definition of information functions perfectly well and correctly elucidates what information is; moreover, specializations of this definition to various theories illustrate the differences in different types of information.
The third and final chapter of the opening part, “Information, Communication, and Manipulability,” by Olimpia Lombardi and Cristian López, aims at supplying adequate criteria to identify information in a communicational context. For this purpose, the chapter begins by considering the different interpretations of Shannon’s formalism that can be implicitly or explicitly found in the literature, and the additional challenges raised by the advent of entanglement-assisted communication. This analysis shows that the communication of information is a process that involves a certain idea of causation and the asymmetry implicit in it. On this basis, the authors claim that the manipulability accounts of causation supply the philosophical tools to characterize the transmission of information in a communicational context, and that many conundrums around the concept of information in this context are solved or simply vanish in the light of a manipulability view of information.
Part II begins with Jeffrey Bub’s chapter, “Quantum versus Classical Information.” Bub opens his chapter by stressing that the question “What is quantum information?” has two parts: first, “what is information?” second, “what is the difference between quantum information and classical information?” and he proposes an answer to the second question. With this purpose, Bub begins by supplying a characterization of intrinsic randomness, and then shows that the nonlocal correlations of entangled quantum systems are only possible if the measurement outcomes on the separate systems are intrinsically random events. Then, intrinsic randomness increases the possibilities for information processing, essentially because new sorts of correlations are possible that cannot occur in a classic world. On this basis, the author concludes that intrinsic randomness marks the difference between quantum and classical information: quantum information is a type of information that is only possible in a world in which there are intrinsically random events.
In the following chapter of Part II, “Quantum Information and Locality,” Dennis Dieks begins by recalling that the surprising aspects of quantum information are due to two distinctly non-classical features of the quantum world: first, different quantum states need not be orthogonal, and, second, quantum states may be entangled. He focuses on the concept of entanglement, since it leads, via non-locality, to those forms of communication that go beyond what is classically possible. In particular, he analyzes the significance of entanglement for the basic physical concepts of “particle” and of “localized physical system.” According to the author, in general the structure of quantum mechanics is at odds with an interpretation in terms of particles, which may be localized. This leads him to the conclusion that quantum mechanics is best seen as not belonging to the category of space-time theories: the resulting picture of the quantum world is relevant for understanding in what sense quantum theory is non-local, and this in turn sheds light on the novel aspects of quantum information.
In his chapter, “Pragmatic Information in Quantum Mechanics,” Juan Roederer argues that information is essentially a pragmatic notion. The chapter begins by distinguishing between two categories of interactions between bodies or systems: force-driven, which operates in the entire spatial-temporal domain, and information-driven, which leads to the definition of information as a pragmatic concept. Pragmatic information is defined as that which represents a physical, causal, and univocal correspondence between a pattern and a specific macroscopic change mediated by some complex interaction mechanism. On the basis of this definition, pragmatic information in itself does not operate in the quantum domain. According to the author, to the extent that information is pragmatic, talking about inaccessible or hidden information in quantum states makes no sense: quantum mechanics can only provide real – pragmatic – information by means of natural or deliberate macroscopic imprints left by a composite quantum system, which as a single whole interacts irreversibly with the surrounding macroscopic world.
In the last chapter of Part II, “Interpretations of Quantum Theory: A Map of Madness,” Adán Cabello stresses the fact that, at present, physicists do not yet agree about what quantum theory is about, and argues that it is urgent to solve this problem. In order to contribute to the solution, he classifies the interpretations of quantum theory into two types, according to whether the probabilities of measurement outcomes are determined by intrinsic properties of the observed system or not. Cabello considers that these two types of interpretations are so radically different that there must be experiments that, when analyzed outside the framework of quantum theory, lead to different empirically testable predictions.
Part III, devoted to probabilities and correlations, begins with the chapter “On the Tension between Ontology and Epistemology in Quantum Probabilities,” where Amit Hagar proposes a physical underpinning of quantum probabilities, which is dynamical, finitist, operational, and objective. According to this operationalist view, which dispels the metaphysics that surrounds the quantum state, finite-resolution measurement outcomes are taken as primitive and basic building blocks of the theory, and quantum probabilities are objective dynamical transition probabilities between finite-resolution measurement results. As a consequence, nonrelativistic quantum mechanics is seen as a phenomenological, “effective” theory, whose mathematical structure – the Hilbert space – rather than a fundamental structure that requires interpretation, is a tool for computing the probabilities of future states of an underlying deterministic and discrete process, from the inherently and objectively limited knowledge we have about it. According to the author, this view of probabilities can qualify as an objective alternative to the subjective view that the quantum information theoretic approach adheres to.
In his chapter, “Inferential versus Dynamical Conceptions of Physics,” David Wallace addresses the issue of probabilities in physics by contrasting two possible attitudes towards a given branch of physics: inferential, as concerned with an agent’s ability to make predictions given finite information, and dynamical, as concerned with the dynamical equations governing particular degrees of freedom. He contrasts these attitudes in classical statistical mechanics, in quantum mechanics, and in quantum statistical mechanics. In this last case, he argues that the quantum-mechanical and statistical-mechanical aspects of the question become inseparable. On this basis, the conclusion of the chapter is that the particular attitude adopted – whether to conceive of a given field in physics as a form of inference or as a study of dynamics – plays a central role in the foundations of quantum theory, and the exact same role in the foundations of statistical mechanics once it is understood quantum mechanically.
The chapter “Classical Models for Quantum Information,” by Federico Holik and Gustavo Martín Bosyk, faces the question about the ontological status of quantum information. The first part of the chapter emphasizes the existence of probabilistic models that go beyond the classical and quantal realms, and the possibility of performing informational protocols in those models. On this basis, the authors argue that a generalized information theory can be conceived. In the second part, the question about the ontological reference of those probabilistic models is addressed. For this purpose, the authors recall the existence of many examples of physical systems built by means of an essentially classical ontology, but that are modeled by formal structures with quantum features. Their significance relies on the fact that they can be used to perform quantum information protocols. This fact points to the need of exploring the ontological implications of those simulations for the concept of quantum information.
The last chapter of Part III, “On the Relative Charecter of Quantum Corrlations,” by Ángel Luis Plastino, Guido Bellomo, and Ángel Ricardo Plastino , revisits the concepts of entanglement and discord from a generalized perspective that focuses on the relational aspect of the term “correlation” with respect to the states and observables involved. From the fact that the concept of correlation is inherently relative to the non-unique partition of a system into subsystems, the authors favor a description-dependent view of the quantum correlations that provides what they call a second stage of relativity. On this basis, they propose generalized definitions for entanglement and discord. Moreover, the authors argue that the relative character of quantum correlations imposes restrictions on the classical appearance of the quantum. In particular, they prove that some types of quantum correlations may appear as classical correlations when certain relevant observables in a larger Hilbert space are measured. Therefore, the classical appearance of the quantum world is also relative to a given description.
As this brief overview shows, the question about what quantum information is can be addressed from many different perspectives, some of them complementary, others conflicting with each other. This plurality precisely reveals to what extent the community of quantum physicists and philosophers of physics is far from a consensus about the answer of that question. This volume is intended as a contribution to the discussion about the conceptual foundations of an exciting field like quantum information theory.
