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Philosophy of Science

A Philosopher Looks at Quantum Information Theory

Amit Hagar

Published Oct 1, 2003• 23 citations
Publisher

Abstract

Recent suggestions to supply quantum mechanics (QM) with realistic foundations by reformulating it in light of quantum information theory (QIT) are examined and are found wanting by pointing to a basic conceptual problem that QIT itself ignores, namely, the measurement problem. Since one cannot ignore the measurement problem and at the same time pretend to be a realist, as they stand, the suggestions to reformulate QM in light of QIT are nothing but instrumentalism in disguise.

DOI
10.1086/378863

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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.

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Jonte R. Hance, Sabine Hossenfelder

Abstract We summarise different aspects of the measurement problem in quantum mechanics. We argue that it is a real problem which requires a solution, and identify the properties a theory needs to solve the problem. We show that no current interpretation of quantum mechanics solves the problem, and that, being interpretations rather than extensions of quantum mechanics, they cannot solve it. Finally, we speculate what a solution of the measurement problem might be good for.

arXiv:2206.10445•Journal of Physics Communications•Sep 30, 2022•2 citations
Recent suggestions to supply quantum mechanics (QM) with realistic foundations by reformulating it in light of quantum information theory (QIT) are examined and are found wanting by pointing to a basic conceptual problem that QIT itself ignores, namely, the measurement problem. Since one cannot ignore the measurement problem and at the same time pretend to be a realist, as they stand, the suggestions to reformulate QM in light of QIT are nothing but instrumentalism in disguise.
Quantum Information Theory (QIT) has emerged as one of the most influential fields in modern science, combining the principles of quantum mechanics with classical information theory. It forms the theoretical foundation of advanced technologies such as quantum computing, quantum communication, and quantum cryptography. Despite remarkable progress in these areas, the measurement problem remains a fundamental conceptual and practical challenge. Measurement in quantum mechanics plays a dual role: it enables information extraction while simultaneously disturbing the quantum system. This paper presents a detailed study of the measurement problem within the framework of quantum information theory. It examines the role of measurement in quantum state evolution, the effects of entanglement and decoherence, and the impact on information processing tasks. The paper also discusses existing theoretical approaches and highlights the importance of resolving measurement-related issues for the future development of quantum technologies.
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.
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.