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Article Dans Une Revue International Journal of Foundations of Computer Science Année : 2012

The Physical Church-Turing Thesis and the Principles of Quantum Theory

Résumé

As was emphasized by Deutsch, quantum computation shatters complexity theory, but is innocuous to computability theory. Yet Nielsen and others 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.

Dates et versions

hal-00944482 , version 1 (10-02-2014)

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Pablo Arrighi, Gilles Dowek. The Physical Church-Turing Thesis and the Principles of Quantum Theory. International Journal of Foundations of Computer Science, 2012, 23 (5), pp.1131-1146. ⟨10.1142/S0129054112500153⟩. ⟨hal-00944482⟩
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