Finite automata models of quantized systems

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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.pd
  f

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Information is physical

• Continuum theory and deterministic chaos
• Possible speedups in quantum computing
• Suggestions to trespass the Turing barrier

3
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

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Logic of 4-state automata
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Recent developments

• Characterizazion of types of Complementarity
• Simulation, universality and complementarity
• Automaton partition logic
• (C. S. Calude, E. Calude, B. Khoussainov,M.Schall
  er, M. Lipponen, K.S.)

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Generalized urn models (Wright, 1978)
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Logical equivalence of automata and generalized
urn models
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Reversible automata

• Combined transition and output functions are
  bijective, evolution is a permutation

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Value definiteness in qm?

• Nonexistence of two-valued measures (truth
  values) in quantized systems of Hilbert space
  dimension gt2

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Counterfactual Automata
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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)

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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.