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Non-Markovian quantum dynamics: local versus nonlocal.

Dariusz Chruściński¹, Andrzej Kossakowski

¹Institute of Physics, Nicolaus Copernicus University, Grudziadzka 5/7, 87-100 Toruń, Poland.

Physical Review Letters

|April 7, 2010

Summary

We analyze non-Markovian evolution in open quantum systems. Our findings show that dynamics can be described by either nonlocal or local equations, revealing key aspects of quantum memory effects.

Area of Science:

Quantum Physics
Quantum Information Science

Background:

Open quantum systems exhibit complex dynamics.
Non-Markovian evolution is crucial for understanding quantum information processing.

Purpose of the Study:

To analyze the non-Markovian evolution of open quantum systems.
To explore complementary descriptions of quantum dynamics.

Main Methods:

Analysis of dynamical maps.
Development of nonlocal master equations with memory kernels.
Formulation of time-local equations.

Main Results:

Any dynamical map can be described by nonlocal or time-local equations.
These descriptions are complementary, with complexity shifting between them.

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The time-local generator retains memory of the initial time, defining non-Markovianity.

Singularities in the generator can lead to phenomena like coherence revival and entanglement dynamics.

Conclusions:

Non-Markovian quantum dynamics can be equivalently described by nonlocal or time-local formalisms.
The time-local approach inherently captures memory effects essential for non-Markovianity.
Generator singularities in the local description are linked to observable quantum phenomena.