The physical Church-Turing thesis and the principles of quantum theory

Abstract : Notoriously, quantum computation shatters complexity theory, but is innocuous to computability theory. Yet several works have shown how quantum theory as it stands could breach the physical Church-Turing thesis. We draw a clear line as to when this is the case, in a way that is inspired by Gandy. Gandy formulates postulates about physics, such as homogeneity of space and time, bounded density and velocity of information --- and proves that the physical Church-Turing thesis is a consequence of these postulates. We provide a quantum version of the theorem. Thus this approach exhibits a formal non-trivial interplay between theoretical physics symmetries and computability assumptions.
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https://hal.archives-ouvertes.fr/hal-00944544
Contributeur : Nicolas Peltier <>
Soumis le : lundi 10 février 2014 - 17:01:06
Dernière modification le : jeudi 11 octobre 2018 - 08:48:04

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  • HAL Id : hal-00944544, version 1
  • ARXIV : 1102.1612

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Pablo Arrighi, Gilles Dowek. The physical Church-Turing thesis and the principles of quantum theory. QIPC, 2011, Zurich, Switzerland. Local proceedings, 2011. 〈hal-00944544〉

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