Cave! Still incomplete.
Title: Why do we care about violating Bell Inequalities?
With Natasha Oughton
Abstract: The Information Causality principle was proposed to re-derive the Tsirelson bound, an upper limit on the strength of quantum correlations, and has been suggested as a candidate law of nature. The principle states that the Shannon information about Alice’s distant database gained by Bob after receiving an m bit message cannot exceed m bits, even when Alice and Bob share non-local resources. As originally formulated, it can be shown that the principle is violated exactly when the strength of the shared correlations exceeds the Tsirelson bound. However, we demonstrate here that when an alternative measure of information, one of the Renyi measures, is chosen, the Information Causality principle no longer arrives at the correct value for the Tsirelson bound. We argue that neither the assumption of particular ‘intuitive’ properties of uncertainties measures, nor pragmatic choices about how to optimise costs associated with communication, are sufficient to motivate uniquely the choice of the Shannon measure from amongst the more general Renyi measures. We conclude that the dependence of the success of Information Causality on mere convention undermines its claimed significance as a foundational principle.
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Title: Why do we care about violating Bell Inequalities?
Abstract: High energy experiments present an exciting new regime in which to explore the violation of Bell inequalities by nature. There are two main reasons why one is interested in Bell inequality violation. The first is that---for suitable experimental configurations---Bell inequality violation can indicate the failure of the condition of Local Causality, which condition is a natural way of capturing the desideratum of no superluminal action-at-a-distance. The second is that Bell inequality violation is an Entanglement Witness. I review both of these reasons for interest, and suggest that high energy experiments plausibly involve the latter rather more than the former, at least as currently configured.
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Title: Black Hole Entropy is Thermodynamic Entropy
With Carina Prunkl
Abstract: The comparison of geometrical properties of black holes with classical thermodynamic variables reveals surprising parallels between the laws of black hole mechanics and the laws of thermodynamics. Since Hawking's discovery that black holes when coupled to quantum matter fields emit radiation at a temperature proportional to their surface gravity, the idea that black holes are genuine thermodynamic objects with a well-defined thermodynamic entropy has become more and more popular. Surprisingly, arguments that justify this assumption are both sparse and rarely convincing. Most of them rely on an information-theoretic interpretation of entropy, which in itself is a highly debated topic in the philosophy of physics. We discuss some of the pertinent arguments that aim at establishing the identity of black hole surface area (times a constant) and thermodynamic entropy and show why these arguments are not satisfactory. We then present a simple model of a Black Hole Carnot cycle to establish that black hole entropy is genuine thermodynamic entropy which does not require an information-theoretic interpretation.
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With Owen Maroney
Abstract: We have a conundrum. The physical basis of information is clearly a highly active research area. Yet the power of information theory comes precisely from separating it from the detailed problems of building physical systems to perform information-processing tasks. Developments in quantum information over the last two decades seem to have undermined this separation, leading to suggestions that information is itself a physical entity and must be part of our physical theories, with resource-cost implications. We will consider a variety of ways in which physics seems to affect computation, but will ultimately argue to the contrary: rejecting the claims that information is physical provides a better basis for understanding the fertile relationship between information theory and physics. Instead, we will argue that the physical resource costs of information processing are to be understood through the need to consider physically embodied agents for whom information-processing tasks are performed. Doing so sheds light on what it takes for something to be implementing a computational or information-processing task of a given kind.
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Title: On the Thermodynamical Cost of Some Interpretations of Quantum Theory
With Carina Prunkl
Abstract: Recently, Cabello et al. (2016) claim to have proven the existence of an empirically verifiable difference between two broad classes of quantum interpretations. On the basis of three seemingly uncontentious assumptions, (i) the possibility of randomly selected measurements, (ii) the finiteness of a quantum system's memory, and (iii) the validity of Landauer's principle, and further, by applying computational mechanics to quantum processes, the authors arrive at the conclusion that some quantum interpretations (including central realist interpretations) are associated with an excess heat cost and are thereby untenable—or at least—that they can be distinguished empirically from their competitors by measuring the heat produced. Here, we provide an explicit counterexample to this claim and demonstrate that their surprising result can be traced back to a lack of distinction between system and external agent. By drawing the distinction carefully, we show that the resulting heat cost is fully accounted for in the external agent, thereby restoring the tenability of the quantum interpretations in question.
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Title: Bell on Bell's Theorem: The Changing Face of Nonlocality
With Harvey Brown
Abstract: Between 1964 and 1990, the notion of nonlocality in Bell's papers underwent a profound change as his nonlocality theorem gradually became detached from quantum mechanics, and referred to wider probabilistic theories involving correlations between separated beables. The proposition that standard quantum mechanics is itself nonlocal (more precisely, that it violates ‘local causality’) became divorced from the Bell theorem per se from 1976 on, although this important point is widely overlooked in the literature. In 1990, the year of his death, Bell would express serious misgivings about themathematical form of the local causality condition and leave ill-defined the issue of the consistency between special relativity and violation of the Bell-type inequality. In our view, the significance of the Bell theorem, in both its deterministic and stochastic forms, can only be fully understood by taking into account the fact that a fully Lorentz covariant version of quantum theory, free of action at a distance, can be articulated in the Everett interpretation.
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Title: The Philosophy of Quantum Information
Abstract: An introductory discussion of what quantum information theory is, and what conceptual puzzles it presents. Also, how some of these might be resolved.
Author draft .pdf
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Title: Quantum vs Macro- Realism: What does the Legget-Garg Inequality actually test? With Owen Maroney
Abstract: Macroscopic Realism (MR) says that a macroscopic system is always determinately in one or other of the macroscopically distinguishable states available to it. The Leggett-Garg (LG) inequality was derived to allow experimental test of whether or not this doctrine is true; it is also often thought of as a temporal version of a Bell-inequality. Despite recent interest in the inequality, controversy remains regarding what would be shown by its violation. Here we resolve this controversy, which arises due to an insufficiently general and model-independent approach to the question so far. We argue that LG's initial characterisation of MR does not pick out a particularly natural realist position, so we articulate an operationally well-defined and well-motivated position in its place. We show that much weaker conditions than LG's are sufficient to derive the inequality: in the first instance, its violation only demonstrates that certain measurements fail to be non-disturbing at the operational level. We articulate three distinct species of MR-ist position, and argue that it is only the first of these which can be refuted by LG inequality violation. This first position is an attractive one, so ruling it out remains of interest, however. A crucial role is played in LG's argument by the assumption of noninvasive measurability. We show that this notion is ambiguous between the weaker notion of disturbance at the operational level, and the stronger notion of invasiveness at the ontic level of properties of the system. Ontic noninvasiveness would be required to rule out MR per se but this property is not entailed by MR, and its presence cannot be established in a model-independent way. It follows that despite the formal parallels, Bell's and LG's inequalities are not methodologically on a par. We close with some reflections on the implications of our analysis for the pedagogy of quantum superposition.
This paper was accepted by The British Journal for the Philosophy of Science in 2015, but its publication was delayed by, amongst other things, the journal reducing its word limit for accepted articles whilst this paper was under review.
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Title: Probabilities in Realist Views of Quantum Mechanics Abstract: I discuss the nature of probabilities within realist approaches to quantum mechanics, focussing on three principle examples: Dynamical Collapse theories (specifically the Ghiradri-Rimini-Weber theory), the de Broglie-Bohm pilot wave theory, and the Everett interpretation. The discussion is organised by looking at the different answers that are given within each approach to two questions: 1. In what manner does probability enter the theory? and 2. What is the status of the standard probabilistic rule—the Born Rule—in the theory?
The original version of this paper was shortened for publication in the edited collection; my preferred longer (canonical) version is available here
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Title: Quantum Mechanics on Spacetime I: Spacetime State Realism
With David Wallace
Abstract: What ontology does realism about the quantum state suggest? The main extant view in contemporary philosophy of physics is wave-function realism. We elaborate the sense in which wave-function realism does provide an ontological picture, and defend it from certain objections that have been raised against it. However, there are good reasons to be dissatisfied with wave-function realism, as we go on to elaborate. This motivates the development of an opposing picture: what we call spacetime state realism, a view which takes the states associated to spacetime regions as fundamental. This approach enjoys a number of beneficial features, although, unlike wave-function realism, it involves non-separability at the level of fundamental ontology. We investigate the pros and cons of this non-separability, arguing that it is a quite acceptable feature, even one which proves fruitful in the context of relativistic covariance. A companion paper discusses the prospects for combining a spacetime-based ontology with separability, along lines suggested by Deutsch and Hayden.
N.B. A short version of the argument of the `companion paper' mentioned is given in `Nonlocality and Gauge Freedom' below. (But also N.B. that we do not intend to suggest -despite our phrasing in that paper - that the time-dependent transformations we there introduce are symmetries. In any case, the main argument goes through even restricting only to the time independent transformations. In the main, this observation serves to rebut Deutsch's objection to our argument.) The companion paper will still appear in due course...
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Title: Rabid Dogma? Comments on Bub and Pitowsky
Abstract: I critically discuss Jeff Bub and Itamar Pitowsky's proposal of an 'information theoretic' interpretation of quantum theory which hopes to circumvent the measurement problem. I argue that if the interpretation is to be a realist one (as they hope), then it amounts to an under-specified modal or hidden variables interpretation; and that in any case, their attempt to avoid the measurement problem fails: Bub and Pitowsky's argument equivocates between considering the spread of pre- and post-measurement probability distributions and considering dynamics which governs the possible to actual transition. To avoid the measurement problem they need to show that we should not demand the latter, whilst the considerations they adduce only address the former.
N.B. Readers often seem to miss footnote 4. Don't miss it: it is very important! Back
Title: Building with Quantum Correlations
With H.R. Brown
Abstract: ‘Correlations without correlata’ is an influential way of thinking of quantum entanglement as a form primitive correlation which nonetheless maintains locality of quantum theory. A number of arguments have sought to suggest that such a view leads either to internal inconsistency or to conflict with the empirical predictions of quantum mechanics. Here we explicate and provide a partial defence of the notion, arguing that these objections import unwarranted conceptions of correlation properties as hidden variables. A more plausible account sees the properties in terms of Everettian relative states. The ontological robustness of entanglement is also defended from recent objections.
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Title: Quantum Bayesianism:A Study Abstract: The Bayesian approach to quantum mechanics of Caves, Fuchs and Schack is presented. Its conjunction of realism about physics along with anti-realism about much of the structure of quantum theory is elaborated; and the position defended from common objections: that it is solipsist; that it is too instrumentalist; that it cannot deal with Wigner's friend scenarios. Three more substantive problems are raised: Can a reasonable ontology be found for the approach? Can it account for explanation in quantum theory? Are subjective probabilities on their own adequate in the quantum domain? The first question is answered in the affirmative, drawing on elements from Nancy Cartwright's philosophy of science. The second two are not: it is argued that these present outstanding difficulties for the project. A quantum Bayesian version of Moore's paradox is developed to illustrate difficulties with the subjectivist account of pure state assignments.
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Title: Information, Immaterialism, Instrumentalism: Old and New in Quantum Information Abstract: In this paper I reflect on how some old and familiar philosophical themes play out in the new field of quantum information. These themes are immaterialism and instrumentalism; and we shall see that they lie at the heart of some of the more intriguing prospects that quantum information theory presents: Does quantum information finally help us resolve the conceptual conundrums of quantum mechanics? And does the theory indicate a new way of thinking about the world one in which the material as the fundamental subject matter of physical theory is seen to be replaced by the immaterial: information?
We begin by exploring some of the ways in which it has been argued that information talk will aid our understanding of the basic conundrums in quantum mechanics specifically the problems of measurement and non-locality. Hartle (1968) illustrates a common strategy: if the quantum state is understood to represent information rather than an objective feature of the world, our troubles seem to disappear. But this strategy proves problematic. It would seem either tacitly to invoke hidden variables, or merely to slide into a form of instrumentalism. Yet instrumentalism is not a particularly edifying interpretive option, nor one that is improved by being re-presented in the garb of the most up-to-date of theories. A further problem for the strategy is noted: the factivity of the term information implies that the objectivity it was the express aim of the approach to avoid is re-introduced. It therefore transpires that if one is to make progress by associating the quantum state with some cognitive state, it must be the state of belief that is chosen, not that of knowledge.
One may avoid the unedifying descent into instrumentalism by focusing instead on the question of whether information-theoretic principles might play the role of providing a perspicuous axiomatic basis for quantum mechanics, as a number of authors have urged (e.g., Fuchs 2002, Clifton et al 2003). Here we investigate Zeilinger s (1999) proposed information-theoretic foundational principle for quantum mechanics. His hope is to explain the appearance of intrinsic randomness and entanglement in the theory; and ultimately to answer Wheeler s (1990) question Why the quantum? in a way congenial to the Bohrian intuition that the structure of quantum theory is a consequence of limitations of what can be said about the world. This approach is assessed and found wanting: the Foundational Principle cannot, unfortunately, achieve the results Zeilinger wishes.
Finally, the links are explored between Zeilinger s programme, informational immaterialism and the remark infamously attributed to Bohr: There is no quantum world . It is suggested that this remark is best understood as an example of semantic ascent; and it becomes clear that moves towards immaterialism are by no means supported by such semantic ascent.
Available as .pdf.
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Title: Philosophical Aspects of Quantum Information Theory Abstract: Quantum information theory represents a rich subject of discussion for those interested in the philosphical and foundational issues surrounding quantum mechanics for a simple reason: one can cast its central concerns in terms of a long-familiar question: How does the quantum world differ from the classical one? Moreover, deployment of the concepts of information and computation in novel contexts hints at new (or better) means of understanding quantum mechanics, and perhaps even invites re-assessment of traditional material conceptions of the basic nature of the physical world. In this paper I review some of these philosophical aspects of quantum information theory, begining with an elementary survey of the theory seeking to highlight some of the principles and heuristics involved. We move on to a discussion of the nature and definition of quantum information and deploy the findings in discussing the puzzles surrounding teleportation. The final two sections discuss, respectively, what one might learn from the development of quantum computation (both about the nature of quantum systems and about the nature of computation) and consider the impact of quantum information theory on the traditional foundational questions of quantum mechanics (treating of the views of Zeilinger, Bub and Fuchs, amongst others).
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Title: Why Special Relativity Should Not be a Template for a Fundamental Reformulation of Quantum Mechanics With H.R. Brown Abstract: In a comparison of the principles of special relativity and of quantum mechanics, the former theory is marked by its relative economy and apparent explanatory simplicity. A number of theorists have thus been led to search for a small number of postulates---essentially information theoretic in nature---that would play the role in quantum mechanics that the relativity principle and the light postulate jointly play in Einstein's 1905 special relativity theory. The purpose of the present paper is to resist this idea, at least in so far as it is supposed to reveal the fundamental form of the theory. It is argued that the methodology of Einstein's 1905 theory represents a victory of pragmatism over explanatory depth; and that its adoption only made sense in the context of the chaotic state state of physics at the start of the 20th century---as Einstein well knew.
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Title: The Grammar of Teleportation Abstract: 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.
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Title: Non-locality and Gauge Freedom in Deutsch and Hayden's Formulation of Quantum Mechanics With D. Wallace Abstract: Deutsch and Hayden have proposed an alternative formulation of quantum mechanics which is completely local. We argue that their proposal must
be understood as having a form of `gauge freedom' according to which
mathematically distinct states are physically equivalent. Once this
gauge freedom is taken into account, their formulation is no longer
local.
N.B. This paper, oddly enough, was published again in the succeeding issue of the journal. (`The paper so good they published it twice'?) Back
Title: Proper and Improper Separability With H.R. Brown Abstract: The distinction between proper and improper mixtures is a staple of the discussion of foundational questions in quantum mechanics. Here we note an analogous distinction in the context of the theory of entanglement. The terminology of `proper' versus `improper' separability is proposed to mark the distinction.
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Title: Nonlocality and Information Flow: The Approach of Deutsch and Hayden Abstract: Deutsch and Hayden claim to have provided an account of quantum mechanics which is particularly local, and which clarifies the nature of information transmission in entangled quantum systems. In this paper, a perspicuous description of their formalism is offered and their claim assessed. It proves essential to distinguish, as Deutsch and Hayden do not, between two ways of interpreting the formalism. On the first, conservative, interpretation, no benefits with respect to locality accrue that are not already available on either an Everettian or a statistical interpretation; and the conclusions regarding information flow are equivocal. The second, ontological, interpretation, offers a framework with the novel feature that global properties of quantum systems are reduced to local ones; but no conclusions follow concerning information flow in more standard quantum mechanics.
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Title: Quantum Computers: The Church-Turing Hypothesis versus the Turing Principle Abstract: Following the development of quantum computers, a question has arisen regarding the relation between the basis of the classical theory of computation and the quantum theory. Here I argue against Deutsch's claim that a physical principle, the Turing Principle, underlies the famous Church-Turing hypothesis. I also discuss the computational analogy and emphasise a certain line of argument suggesting it may be misplaced. Finally, I assess Deutsch's claims for the dependence of mathematics upon empirical science, claims that arise as a consequence of his conception of computation and his adherence to the computational analogy.
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Title: Entanglement and Relativity Abstract:
This paper surveys some of the questions that arise
when we consider how entanglement and relativity are related via the notion of non-locality.
We begin by reviewing the role of entangled states in Bell inequality violation and question whether the associated notions of non-locality lead to problems with relativity. The use of entanglement and wavefunction collapse in Einstein's famous incompleteness argument is then considered, before we go on to see how the issue of non-locality is transformed if one considers quantum mechanics without collapse to be a complete theory, as in the Everett interpretation.
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Title: The Applicability of Shannon Information in Quantum Mechanics and Zeilinger's Foundational Principle Abstract: Recently, Brukner and Zeilinger have presented a number of arguments suggesting that the Shannon information is not well defined as a measure of information in quantum mechanics. If established, this result would be highly significant, as the Shannon information is fundamental to the way we think about information not only in classical but also in quantum information theory. On consideration, however, these arguments are found unsuccessful; I go on to suggest how they might be arising as a consequence of Zeilinger s proposed foundational principle for quantum mechanics.
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Title: On a Supposed Conceptual Inadequacy of the Shannon Information in Quantum Mechanics Abstract: Recently, Brukner and Zeilinger (2001) 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 measure, I(p), 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.