Complexity in Dynamics and Computation View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2001

AUTHORS

Masanori Ohya

ABSTRACT

A new description of chaos in both classical and quantum dynamical systems is discussed in the context of information dynamics, which is called the chaos degree. The algorithm computing this degree is shown. Quantum algorithm solving the SAT problem, on of the NP complete problems, is studied and it is discussed that the SAT problem can be solved in polynomial time when a certain mixture of two orthogonal vectors is physically detected. More... »

PAGES

293-306

References to SciGraph publications

  • 1987-12. Dynamical entropy ofC* algebras and von Neumann algebras in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1996-03. Entropy functionals of Kolmogorov-Sinai type and their limit theorems in LETTERS IN MATHEMATICAL PHYSICS
  • 1983-11. Note on quantum probability in LETTERE AL NUOVO CIMENTO (1971-1985)
  • 1997-02. Dynamical Entropy Through Quantum Markov Chains in OPEN SYSTEMS AND INFORMATION DYNAMICS
  • 1981-12. Absolutely continuous measures for certain maps of an interval in PUBLICATIONS MATHÉMATIQUES DE L'IHÉS
  • 1998-01. Complexities and Their Applications to Characterization of Chaos in INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • 1999-02. Compound Channels, Transition Expectations, and Liftings in APPLIED MATHEMATICS & OPTIMIZATION
  • 1991. Information dynamics and its applications to optical communication processes in QUANTUM ASPECTS OF OPTICAL COMMUNICATIONS
  • 1999-03. Fundamentals of Quantum Mutual Entropy and Capacity in OPEN SYSTEMS AND INFORMATION DYNAMICS
  • 1993. Deterministic Chaos in Infinite Quantum Systems in NONE
  • 1995. State Change, Complexity and Fractal in Quantum Systems in QUANTUM COMMUNICATIONS AND MEASUREMENT
  • 1974-09. Positivity of the K-entropy on non-abelian K-flows in PROBABILITY THEORY AND RELATED FIELDS
  • 1975-07. Entropy for automorphisms of II1 von neumann algebras in ACTA MATHEMATICA
  • 1997. Information Dynamics and Open Systems, Classical and Quantum Approach in NONE
  • 1997-04. Complexity, Fractal Dimension for Quantum States in OPEN SYSTEMS AND INFORMATION DYNAMICS
  • 2000-03. NP Problem in Quantum Algorithm in OPEN SYSTEMS AND INFORMATION DYNAMICS
  • 1977-02. Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1993. Quantum Entropy and Its Use in NONE
  • 1997-11. Dynamical Formulation of Quantum Level Statistics in OPEN SYSTEMS AND INFORMATION DYNAMICS
  • 1998. Foundation of Entropy, Complexity and Fractals in Quantum Systems in PROBABILITY TOWARDS 2000
  • Book

    TITLE

    Recent Developments in Infinite-Dimensional Analysis and Quantum Probability

    ISBN

    978-94-010-3842-3
    978-94-010-0842-6

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-94-010-0842-6_21

    DOI

    http://dx.doi.org/10.1007/978-94-010-0842-6_21

    DIMENSIONS

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