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Hypercomputation and the Physical ChurchTuring Thesis
, 2003
"... A version of the ChurchTuring Thesis states that every e#ectively realizable physical system can be defined by Turing Machines (`Thesis P'); in this formulation the Thesis appears an empirical, more than a logicomathematical, proposition. We review the main approaches to computation beyond Turing ..."
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A version of the ChurchTuring Thesis states that every e#ectively realizable physical system can be defined by Turing Machines (`Thesis P'); in this formulation the Thesis appears an empirical, more than a logicomathematical, proposition. We review the main approaches to computation beyond Turing definability (`hypercomputation'): supertask, nonwellfounded, analog, quantum, and retrocausal computation. These models depend on infinite computation, explicitly or implicitly, and appear physically implausible; moreover, even if infinite computation were realizable, the Halting Problem would not be a#ected. Therefore, Thesis P is not essentially di#erent from the standard ChurchTuring Thesis.
Quantum Hypercomputation—Hype or Computation?
, 2007
"... A recent attempt to compute a (recursion–theoretic) non–computable function using the quantum adiabatic algorithm is criticized and found wanting. Quantum algorithms may outperform classical algorithms in some cases, but so far they retain the classical (recursion–theoretic) notion of computability. ..."
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A recent attempt to compute a (recursion–theoretic) non–computable function using the quantum adiabatic algorithm is criticized and found wanting. Quantum algorithms may outperform classical algorithms in some cases, but so far they retain the classical (recursion–theoretic) notion of computability. A speculation is then offered as to where the putative power of quantum computers may come from.
Quantum Information Theory and . . . Quantum Mechanics
, 2004
"... This thesis is a contribution to the debate on the implications of quantum information theory for the foundational problems of quantum mechanics. In Part I an attempt is made to shed some light on the nature of information and quantum information theory. It is emphasized that the everyday notion of ..."
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This thesis is a contribution to the debate on the implications of quantum information theory for the foundational problems of quantum mechanics. In Part I an attempt is made to shed some light on the nature of information and quantum information theory. It is emphasized that the everyday notion of information is to be firmly distinguished from the technical notions arising in information theory; noun, hence does not refer to a particular or substance. The popular claim ‘Information is Physical ’ is assessed and it is argued that this proposition faces a destructive dilemma. Accordingly, the slogan may not be understood as an ontological claim, but at best, as a methodological one. A novel argument is provided against Dretske’s (1981) attempt to base a semantic notion of information on ideas from information theory. The function of various measures of information content for quantum systems is explored and the applicability of the Shannon information in the quantum context maintained against the challenge of Brukner and Zeilinger (2001). The phenomenon of quantum teleportation is then explored as a case study serving to emphasize the value of