*Cave!* Still incomplete: More electronic versions of papers to appear in due course! (12.04.08)

**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.

**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.

**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).

**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.

**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 *in*dependent 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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.