While the inclusion of information theoretical concepts into (quantum)\nphysics has shown enormous success in recent years, the ontology of information\nremains puzzling. Therefore, this thesis aims to contribute to\nthe debate about the ontological status of information in physics. Most\nof the recent debates have focused on syntactic information measures\nand especially Shannon Information, a concept originally stemming from\nCommunication Theory. This thesis incorporates another syntactic information\nmeasure, the so far largely underrepresented notion of Algorithmic\nInformation or Kolmogorov Complexity, a concept often applied\nin Computer Science. Shannon Information and Kolmogorov Complexity\nare linked through Coding Theory and have similar characteristics.\nThrough the comparison of Shannon Information and Kolmogorov Complexity\na framework is developed which analyses the respective information\nmeasures in relation to uncertainty and semantic information. In addition,\nthis framework investigates whether information can be regarded\na material entity and examines to what extent information is conventional.\nIt turns out that in the classical case Shannon Information and\nKolmogorov Complexity are both abstract and highly conventional entities,\nwhich must not be confused with uncertainty and do not bear any\nrelations with semantic information. Virtually the same results are obtained\nin the quantum case, save for the high degree of conventionality;\nit is argued that Quantum Theory constrains the conventional choices of\nthose who wish to use either theory.
While the inclusion of information theoretical concepts into (quantum)\nphysics has shown enormous success in recent years, the ontology of information\nremains puzzling. Therefore, this thesis aims to contribute to\nthe debate about the ontological status of information in physics. Most\nof the recent debates have focused on syntactic information measures\nand especially Shannon Information, a concept originally stemming from\nCommunication Theory. This thesis incorporates another syntactic information\nmeasure, the so far largely underrepresented notion of Algorithmic\nInformation or Kolmogorov Complexity, a concept often applied\nin Computer Science. Shannon Information and Kolmogorov Complexity\nare linked through Coding Theory and have similar characteristics.\nThrough the comparison of Shannon Information and Kolmogorov Complexity\na framework is developed which analyses the respective information\nmeasures in relation to uncertainty and semantic information. In addition,\nthis framework investigates whether information can be regarded\na material entity and examines to what extent information is conventional.\nIt turns out that in the classical case Shannon Information and\nKolmogorov Complexity are both abstract and highly conventional entities,\nwhich must not be confused with uncertainty and do not bear any\nrelations with semantic information. Virtually the same results are obtained\nin the quantum case, save for the high degree of conventionality;\nit is argued that Quantum Theory constrains the conventional choices of\nthose who wish to use either theory.
This thesis is a contribution to the debate on the implications of quantum information theory for the foundations of quantum mechanics. In Part 1, the logical and conceptual status of various notions of information is assessed. It is emphasized that the everyday notion of information is to be firmly distinguished from the technical notions arising in information theory; however it is maintained that in both settings `information' functions as an abstract noun, hence does not refer to a particular or substance (the worth of this point is illustrated in application to quantum teleportation). The claim that `Information is Physical' is assessed and argued to face a destructive dilemma. Accordingly, the slogan may not be understood as an ontological claim, but at best, as a methodological one. The reflections of Bruckner and Zeilinger (2001) and Deutsch and Hayden (2000) on the nature of information in quantum mechanics are critically assessed and some results presented on the characterization of entanglement in the Deutsch-Hayden formalism. Some philosophical aspects of quantum computation are discussed and general morals drawn concerning the nature of quantum information theory. In Part II, following some preliminary remarks, two particular information-theoretic approaches to the foundations of quantum mechanics are assessed in detail. It is argued that Zeilinger's (1999) Foundational Principle is unsuccessful as a foundational principle for quantum mechanics. The information-theoretic characterization theorem of Clifton, Bub and Halvorson (2003) is assessed more favourably, but the generality of the approach is questioned and it is argued that the implications of the theorem for the traditional foundational problems in quantum mechanics remains obscure.
Nihil est in intellectu quod non prius fuerit in sensu. The Physics of Information This book describes the limits for the communication of information with waves. How many ideas can we communicate by writing on a sheet of paper? How well can we hear a concert? How many details can we distinguish in an image? How much data can we get from our internet connection? These are all questions related to the transport of information by waves. Our sensing ability to capture the differences between distinct waveforms dictates the limits of the amount of information that is delivered by a propagating wave. The problem of quantifying this precisely requires a mathematical description and a physical understanding of both the propagation and the communication processes. We focus on the propagation of electromagnetic waves as described by Maxwell's theory of electromagnetism, and on communication as described by Shannon's theory of information. Although our treatment is mostly based on classical field theory, we also consider limiting regimes where the classical theory must give way to discrete quantum formulations. The old question of whether information is physics or mathematics resounds here. Information is certainly described mathematically, but we argue that it also has a definite physical structure. The central theme of this book is that Shannon's information-theoretic limits are natural. They are revealed by observing physical quantities at certain asymptotic scales where finite dimensionality emerges and observational uncertainties are averaged out. These limits are also rigorous, and obey the mathematical rules that govern the model of reality on which the physical theories are based. Shannon's Laws Originally introduced by Claude Elwood Shannon in 1948, and continuing up to its latest developments in multi-user communication networks, information theory describes in the language of mathematics the limits for the communication of information. These limits are operational, of real engineering significance, and independent of the semantic aspects associated with the communication process.
The approach to thinking about information developed in the previous chapter is turned towards the quantum theory. First, some of the characteristic ideas and applications of quantum information theory are presented, then the nature of quantum information itself is discussed. With the correct conception of Shannon information to hand, the dimension of generalisation which the quantum concept occupies is made clear. Quantum information is simply what is produced by a quantum information source. As in the classical case, a piece of information will be an abstract type (a sequence of quantum states), rather than a concrete thing or physical substance. This conception is defended from a number of potential objections which might be raised. With a clear grasp obtained of the relation between quantum information and the world, it proves short work to dissect the slogan `Information is Physical’ and dispatch the prospect of informational immaterialism.
Information is on everyone's lips.It seems that nowadays there is no philosophical or scientific inquiry that cannot benefit from a reformulation in terms of information theory (IT).Quantum theory (QT) is no exception.Indeed, one of the liveliest debates in the foundations of QT concerns the role that information may play in the solution of the well-known problems in the foundations of QT.For instance, one of the hottest discussions concerns quantum non-locality.On the one hand, IT folks stress how, rather than approaching non-local entanglement as an 'embarrassment', IT invites us to see it as a resource for new information-processing protocols.On the other hand, it is unclear how this invitation can contribute to the solution of the problem of accounting for the apparent nonlocality involved in quantum correlations.Christopher G. Timpson's beautiful book is a welcome contribution to this dialectic.It provides an admirable mix of conceptual and technical analysis of the notion of information and critically analyses the most prominent proposals on the table in the debate over the role of IT in the foundations of QT.Although the focus of Timpson's book is quantum information theory (QIT) and the foundations of QT, a considerable component of its basic precepts will be found extremely useful in any branch (be it more philosophical or more scientific) of applied IT.It is because of this additional value that in this review, sometimes to detriment of exhaustiveness, I prefer to concentrate on providing some samples of Timpson's main argumentative line.This should give a better idea of how this volume can represent valuable reading for both specialists in QIT and non-specialists.First things first.In chapter 2, Timpson provides a sharp analysis of the concepts of information.The plural is due to the necessary distinction between information in the everyday sense and information in the technical sense (informationt).Both are abstract mass nouns, but while the former refers to a semantic and epistemic notion, informationt is a physically defined quantity, measured classically by Shannon information.Informationt is usually described as an undefined notion.Contrary to this claim, at the roots of Timpson's analysis is a neat definition: 'Informationt is what is produced by an informationt source that is required to be reproducible at the destination if the transmission is to be counted a success' (22).Although avowedly deflationary, this definition provides a fertile background to dissipate much of the fog around the nature of informationt and its behaviour.It actually turns out that the majority of the results of this book pivots on this very simple definition.Here is a straightforward example.According to the definition above, a successful transmission requires that the message be reproducible at destination.However, what it is said to be repeatable is not the token of a message, but the type.When we talk about something that is transmitted in communication protocols (the so-called pieces of information) we refer to types, i.e. abstracta, rather than to concrete objects.The operation of conceptual cleansing continues when we pass from classical to quantum informationt (chapter 3).An especially noteworthy result is the rejection of the common view that quantum informationt is different in nature from classical informationt.Timpson's methodology allows instead to account for it as an extension of Shannon informationt.In fact, with the template of classical informationt at hand, Timpson reconstructs the notions of quantum informationt source, measure of quantum informationt and piece of quantum informationt, the latter being a sequence of Hilbert space states.
This paper investigates the potential impact of quantum mechanics on Kolmogorov complexity, a fundamental concept in information theory. The core claim is that quantum phenomena, specifically entanglement and superposition, introduce limitations to the compression achievable through Kolmogorov complexity that are absent in the classical framework. We demonstrate through theoretical analysis that certain datasets exhibit compression ratios exceeding those attainable by classical methods, leveraging the unique properties of quantum states. This extends Kolmogorov complexity by incorporating quantum principles, offering a novel perspective on the nature of information and its quantification. The theoretical framework presented here highlights potential discrepancies between classical and quantum notions of information and sets the stage for future research exploring the implications of quantum mechanics for fundamental information theory. We present a novel approach to defining Kolmogorov complexity within a quantum context, focusing on the measurement problem and its effect on the ability to uniquely determine a string. This work doesn't present experimental results; it is a purely theoretical exploration.
Quantum theory describes our universe incredibly successfully. To our classically-inclined brains, however, it is a bizarre description that requires a reimagining of what fundamental reality, or “ontology”, could look like. This thesis examines different ontological features in light of the success of quantum theory, what it requires, and what it rules out. While these investigations are primarily foundational, they also have relevance to quantum information, quantum communication, and experiments on quantum systems. The way that quantum theory describes the state of a system is one of its most unintuitive features. It is natural, therefore, to ask whether a similarly strange description of states is required on an ontological level. This thesis proves that almost all quantum superposition states for d > 3 dimensions must be real—that is, present in the ontology in a well-defined sense. This is a strong requirement which prevents intuitive explanations of the many quantum phenomena which are based on superpositions. A new theorem is also presented showing that quantum theory is incompatible with macro-realist ontologies, where certain physical quantities must always have definite values. This improves on the Leggett-Garg argument, which also aims to prove incompatibility with macro-realism but contains loopholes. Variations on both of these results that are error-tolerant (and therefore amenable to experimentation) are presented, as well as numerous related theorems showing that the ontology of quantum states must be somewhat similar to the quantum states themselves in various specific ways. Extending these same methods to quantum communication, a simple proof is found showing that an exponential number of classical bits are required to communicate a linear number of qubits. That is, classical systems are exponentially bad at storing quantum data. Causal influences are another part of ontology where quantum theory demands a revision of our classical notions. This follows from the outcomes of Bell experiments, as rigorously shown in recent analyses. Here, the task of constructing a native quantum framework for reasoning about causal influences is tackled. This is done by first analysing the simple example of a common cause, from which a quantum version of Reichenbach’s principle is identified. This quantum principle relies on an identification of quantum conditional independence which can be defined in four ways, each naturally generalising a corresponding definition for classical conditional independence. Not only does this allow one to reason about common causes in a quantum experiments, but it can also be generalised to a full framework of quantum causal models (mirroring how classical causal models generalise Reichenbach’s principle). This new definition of quantum causal models is illustrated by examples and strengthened by it’s foundation on a robust quantum Reichenbach’s principle. An unusual, but surprisingly fruitful, setting for considering quantum ontology is found by considering time travel to the past. This provides a testbed for different ontological concepts in quantum theory and new ways to compare classical and quantum frameworks. It is especially useful for comparing computational properties. In particular, time travel introduces non-linearity to quantum theory, which brings (sometimes implicit) ontological assumptions to the fore while introducing strange new abilities. Here, a model for quantum time travel is presented which arguably has fewer objectionable features than previous attempts, while remaining similarly well-motivated. This model is discussed and compared with previous quantum models, as well as with the classical case. Together, these threads of investigation develop a better understanding of how quantum theory affects possible ontologies and how ontological prejudices influence quantum theory.