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Non-Markovian behavior of small and large complex quantum systems
Marko Žnidarič1, Carlos Pineda, Ignacio García-Mata
1Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Cuernavaca, Mexico.
Physical Review Letters
|September 21, 2011
Summary
We precisely calculated the quantum channel for a complex system interacting with a qubit. This reveals non-Markovian behavior and oscillations, even in large environments, offering insights into quantum dynamics.
Area of Science:
- Quantum information science
- Quantum dynamics
- Complex systems theory
Background:
- Understanding quantum channels is crucial for quantum information processing.
- Investigating strong qubit-environment interactions reveals complex dynamics.
- Non-Markovian behavior in quantum systems poses challenges and opportunities.
Purpose of the Study:
- To exactly calculate the quantum channel for a complex system strongly coupled to a qubit.
- To analyze the resulting dynamics, including non-Markovian effects.
- To explore the influence of system properties like eigenvector randomness on the channel.
Main Methods:
- Exact calculation of the quantum channel under the assumption of random eigenvectors.
- Representation of the channel as an isotropic, time-dependent oscillation of the Bloch ball.
- Analysis of contributions from density of states and spectral correlations.
Main Results:
- The quantum channel exhibits isotropic, time-dependent Bloch ball oscillations.
- Non-Markovian behavior is observed, persisting even in the limit of infinite environments.
- The dynamics are shown to arise from two distinct contributions: density of states and spectral correlations.
Conclusions:
- The study provides an exact analytical framework for a specific class of qubit-environment interactions.
- The identified non-Markovian dynamics offer insights into quantum information degradation and preservation.
- Prototype examples for chaotic and regular dynamics illustrate the general findings.
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