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Decoherence and linear entropy increase in the quantum baker's map.

Andrei N Soklakov1, Rüdiger Schack

  • 1Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 9, 2002
PubMed
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The quantum baker's map shows linear entropy increase, matching classical chaos rates. This study uses quantum computing principles and decoherent histories to analyze chaotic systems.

Area of Science:

  • Quantum mechanics
  • Chaos theory
  • Information theory

Background:

  • The baker's map is a model system for studying chaos.
  • Understanding quantum chaos is crucial for quantum computing.
  • Coarse-graining is a technique to simplify complex quantum systems.

Purpose of the Study:

  • To analyze the coarse-grained quantum baker's map.
  • To determine the rate of entropy increase in the quantum system.
  • To connect quantum chaos to classical Kolmogorov-Sinai entropy.

Main Methods:

  • Symbolic representation of the quantum baker's map on N qubits.
  • Application of the decoherent histories formalism for coarse-graining.
  • Asymptotic analysis of the quantum evolution.

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Main Results:

  • The coarse-grained quantum baker's map exhibits linear entropy increase.
  • The rate of entropy increase is given by the Kolmogorov-Sinai entropy of the classical map.
  • The condition of medium decoherence holds asymptotically.

Conclusions:

  • Quantum and classical chaos dynamics are quantitatively linked through entropy increase.
  • The decoherent histories formalism provides a valid method for coarse-graining quantum chaotic systems.
  • This work offers insights into the behavior of quantum information in chaotic environments.