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Finite automata models of quantized systems. conceptual status and outlook Karl Svozil Institut für Theoretische Physik, Technische Universität Wien Wiedner Hauptstrasse 8-10/136, A-1040 Vienna, AUSTRIA http://tph.tuwien.ac.at/~svozil/publ/2002-kyoto.pdf. Information is physical.
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Finite automata models of quantized systems conceptual status and outlook Karl Svozil Institut für Theoretische Physik, Technische Universität Wien Wiedner Hauptstrasse 8-10/136, A-1040 Vienna, AUSTRIA http://tph.tuwien.ac.at/~svozil/publ/2002-kyoto.pdf
Information is physical • Continuum theory and „deterministic chaos“ • Possible speedups in quantum computing • Suggestions to trespass the Turing barrier
Edward F. Moore (1956 ): formalization of complementarity • Quantum complementarity is the feature of certain microphysical systems not to allow the determination of all of its properties with arbitrary precision at once. • Example: Mealy automaton
Recent developments • Characterizazion of types of Complementarity • Simulation, universality and complementarity • Automaton partition logic (C. S. Calude, E. Calude, B. Khoussainov,M.Schaller, M. Lipponen, K.S.)
Reversible automata • Combined transition and output functions are bijective, evolution is a permutation
Value definiteness in qm? Nonexistence of two-valued measures (truth values) in quantized systems of Hilbert space dimension >2
Base n-information in qm • a n-state particle carries exactly one nit of information • k n-state particles carry exactly k nits of information • Realizable by automata {{{1, 2, 3}, {1, 4, 5}, {2, 6, 7}, {3, 8, 9}, {4, 6, 8}, {5, 7, 9}},{{1, 2, 3}, {1, 4, 5}, {2, 6, 7}, {3, 8, 9}, {4, 6, 9}, {5, 7, 8}},{{1,2,3},{{1,4,7},{2,5,8},{3,6,9},{4,5,6},{7,8,9}}, {{1, 6, 9}, {1, 7, 8}, {2, 4, 9}, {2, 5, 7}, {3, 4, 8}, {3, 5, 6}}, {{1, 6, 9}, {1, 7, 8}, {2, 4, 9}, {2, 5, 8}, {3, 4, 7}, {3, 5, 6}}}. (Zeilinger 1999, K.S. 2002)
Applicability • Automata sometimes behave differently than qm; e.g., {{{1},{2},{3,4}},{{1},{2,4},{3}},{{1,4},{2},{3}}}. • ``intrinsic physical properties'' of virtual realities in general, and computer games in particular; the intrinsic ``look and feel'' of computer animated worlds.