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Phys. Rev. Lett. 79, 2915–2918 (1997)

Computable Functions, Quantum Measurements, and Quantum Dynamics

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M. A. Nielsen
Center for Advanced Studies, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131-1156
and Norman Bridge Laboratory of Physics 12-33, California Institute of Technology, Pasadena, California 91125

Received 4 June 1997; published in the issue dated 13 October 1997

We construct quantum mechanical observables and unitary operators which, if implemented in physical systems as measurements and dynamical evolutions, would contradict the Church-Turing thesis which lies at the foundation of computer science. We conclude that either the Church-Turing thesis needs revision, or that only restricted classes of observables may be realized, in principle, as measurements, and that only restricted classes of unitary operators may be realized, in principle, as dynamics.

© 1997 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.79.2915
DOI:
10.1103/PhysRevLett.79.2915
PACS:
89.70.+c, 03.65.Bz