Many Worlds, the Cluster-state Quantum Computer, and the Problem of the Preferred Basis

I argue that the many worlds explanation of quantum computation is not licensed by, and in fact is conceptually inferior to, the many worlds interpretation of quantum mechanics from which it is derived. I argue that the many worlds explanation of quantum computation is incompatible with the recently developed cluster state model of quantum computation. Based on these considerations I conclude that we should reject the many worlds explanation of quantum computation.Comment: Added doi, acknowledgements, miscellaneous typo correction

On the Necessity of Entanglement for the Explanation of Quantum Speedup

In this paper I argue that entanglement is a necessary component for any explanation of quantum speedup and I address some purported counter-examples that some claim show that the contrary is true. In particular, I address Biham et al.'s mixed-state version of the Deutsch-Jozsa algorithm, and Knill & Laflamme's deterministic quantum computation with one qubit (DQC1) model of quantum computation. I argue that these examples do not demonstrate that entanglement is unnecessary for the explanation of quantum speedup, but that they rather illuminate and clarify the role that entanglement does play.Comment: Many clarificatory changes, and improved argumentation. Comments and criticisms are still welcom

Information Causality, the Tsirelson Bound, and the 'Being-Thus' of Things

The principle of `information causality' can be used to derive an upper bound---known as the `Tsirelson bound'---on the strength of quantum mechanical correlations, and has been conjectured to be a foundational principle of nature. To date, however, it has not been sufficiently motivated to play such a foundational role. The motivations that have so far been given are, as I argue, either unsatisfactorily vague or appeal to little if anything more than intuition. Thus in this paper I consider whether some way might be found to successfully motivate the principle. And I propose that a compelling way of so doing is to understand it as a generalisation of Einstein's principle of the mutually independent existence---the `being-thus'---of spatially distant things. In particular I first describe an argument, due to Demopoulos, to the effect that the so-called `no-signalling' condition can be viewed as a generalisation of Einstein's principle that is appropriate for an irreducibly statistical theory such as quantum mechanics. I then argue that a compelling way to motivate information causality is to in turn consider it as a further generalisation of the Einsteinian principle that is appropriate for a theory of communication. I describe, however, some important conceptual obstacles that must yet be overcome if the project of establishing information causality as a foundational principle of nature is to succeed.Comment: '*' footnote added to page 1; 24 pages, 1 figure; Forthcoming in Studies in History and Philosophy of Modern Physic

Is Entanglement Sufficient to Enable Quantum Speedup?

According to the Gottesman-Knill theorem, any quantum algorithm utilising operations chosen exclusively from a particular restricted set are efficiently simulable by a classical computer. Since some of these algorithms involve entangled states, it is commonly concluded that entanglement is insufficient to enable quantum speedup. As I explain, however, the operations belonging to this set are precisely those which will never yield a violation of the Bell inequalities. Thus it should be no surprise that entangled quantum states which only undergo operations in this set are efficiently simulable classically. What the Gottesman-Knill theorem shows us is that it is possible to use an entangled state to less than its full potential. Nevertheless, there is a meaningful sense in which entanglement is sufficient for quantum speedup: an entangled quantum state provides sufficient physical resources to enable quantum speedup, whether or not one elects to use these resources fully.Comment: Only minor changes from last version. Comments and criticisms are welcome. This article has been superseded by arXiv:1310.093

Reflections on the Role of Entanglement in the Explanation of Quantum Computational Speedup

Of the many and varied applications of quantum information theory, perhaps the most fascinating is the sub-field of quantum computation. In this sub-field, computational algorithms are designed which utilise the resources available in quantum systems in order to compute solutions to computational problems with, in some cases, exponentially fewer resources than any known classical algorithm. While the fact of quantum computational speedup is almost beyond doubt, the source of quantum speedup is still a matter of debate. In this paper I argue that entanglement is a necessary component for any explanation of quantum speedup and I address some purported counter-examples that some claim show that the contrary is true. In particular, I address Biham et al.'s mixed-state version of the Deutsch-Jozsa algorithm, and Knill \& Laflamme's deterministic quantum computation with one qubit (DQC1) model of quantum computation. I argue that these examples do not demonstrate that entanglement is unnecessary for the explanation of quantum speedup, but that they rather illuminate and clarify the role that entanglement does play

On the Debate Concerning the Proper Characterisation of Quantum Dynamical Evolution

There has been a long-standing and sometimes passionate debate between physicists over whether a dynamical framework for quantum systems should incorporate not completely positive (NCP) maps in addition to completely positive (CP) maps. Despite the reasonableness of the arguments for complete positivity, we argue that NCP maps should be allowed, with a qualification: these should be understood, not as reflecting 'not completely positive' evolution, but as linear extensions, to a system's entire state space, of CP maps that are only partially defined. Beyond the domain of definition of a partial-CP map, we argue, much may be permitted.Comment: To be presented at the 2012 biennial meeting of the Philosophy of Science Association (PSA), San Diego, Californi

Causality and Complementarity in Kant, Hermann, and Bohr

Kant's doctrine of transcendental idealism, as put forth in the first Critique, is best understood as a conceptual or epistemic doctrine. However critics of the conceptual understanding of transcendental idealism argue that it amounts to an arbitrary stipulation and that it does not do justice to the real ontological distinctions that mattered for Kant. Some stipulations are better than others, however. In this paper I argue that Kant's doctrine, though it should be understood `merely epistemically', is nevertheless full of significance and is motivated through his long-running pre-critical struggle to discover first principles for metaphysical cognition. I further argue that an epistemic understanding of the doctrine of transcendental idealism provides a Kantian with a natural way of understanding the novel epistemic situation presented to us by modern physics and in particular by quantum mechanics. And I argue that considering Kant's philosophy in the light of the challenges posed by quantum mechanics illuminates, in return, several elements of his philosophical framework, notably the principle of causality, the doctrine of synthetic a priori principles in general, and most generally: the conceptual understanding of transcendental idealism itself. I illustrate this via an analysis of the views of the physicist Niels Bohr as well the views of the (neo-)Kantian philosopher Grete Hermann

Wittgenstein on Prior Probabilities

Wittgenstein did not write very much on the topic of probability. The little we have comes from a few short pages of the Tractatus, some 'remarks' from the 1930s, and the informal conversations which went on during that decade with the Vienna Circle. Nevertheless, Wittgenstein's views were highly influential in the later development of the logical theory of probability. This paper will attempt to clarify and defend Wittgenstein's conception of probability against some oft-cited criticisms that stem from a misunderstanding of his views. Max Black, for instance, criticises Wittgenstein for formulating a theory of probability that is capable of being used only against the backdrop of the ideal language of the Tractatus. I argue that on the contrary, by appealing to the 'hypothetical laws of nature', Wittgenstein is able to make sense of probability statements involving propositions that have not been completely analysed. G.H. von Wright criticises Wittgenstein's characterisation of these very hypothetical laws. He argues that by introducing them Wittgenstein makes what is distinctive about his theory superfluous, for the hypothetical laws are directly inspired by statistical observations and hence these observations indirectly determine the mechanism by which the logical theory of probability operates. I argue that this is not the case at all, and that while statistical observations play a part in the formation of the hypothetical laws, these observations are only necessary, but not sufficient conditions for the introduction of these hypotheses

Causality and Complementarity in Kant, Hermann, and Bohr

Kant's doctrine of transcendental idealism, as put forth in the first Critique, is best understood as a conceptual or epistemic doctrine. However critics of the conceptual understanding of transcendental idealism argue that it amounts to an arbitrary stipulation and that it does not do justice to the real ontological distinctions that mattered for Kant. Some stipulations are better than others, however. In this paper I argue that Kant's doctrine, though it should be understood `merely epistemically', is nevertheless full of significance and is motivated through his long-running pre-critical struggle to discover first principles for metaphysical cognition. I further argue that an epistemic understanding of the doctrine of transcendental idealism provides a Kantian with a natural way of understanding the novel epistemic situation presented to us by modern physics and in particular by quantum mechanics. And I argue that considering Kant's philosophy in the light of the challenges posed by quantum mechanics illuminates, in return, several elements of his philosophical framework, notably the principle of causality, the doctrine of synthetic a priori principles in general, and most generally: the conceptual understanding of transcendental idealism itself. I illustrate this via an analysis of the views of the physicist Niels Bohr as well the views of the (neo-)Kantian philosopher Grete Hermann