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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.
Summary
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.
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.
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