On the hybrid Davies like generator for quantum dissipation

Area of Science:

• Quantum mechanics
• Quantum information theory
• Open quantum systems

Background:

• Standard quantum evolution models often assume the Markovian approximation, limiting their applicability to systems with memory effects.
• The Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) generator describes quantum dynamical semigroups but does not inherently account for memory kernels.
• Maintaining complete positivity is crucial for physically realistic quantum evolutions.

Purpose of the Study:

• To develop a quantum evolution framework that extends beyond the Markovian semigroup approximation.
• To incorporate memory effects into quantum dissipation while preserving complete positivity.
• To provide a theoretical model for quantum evolution in open quantum systems with non-Markovian dynamics.

Main Methods:

• A hybrid generator combining a memory kernel for dissipation and a GKLS generator for decoherence was proposed.
• The commutation relations between the memory kernel, GKLS generator, and unitary evolution were analyzed.
• The scheme was illustrated using the example of a single qubit's evolution.

Main Results:

• The proposed hybrid generator allows for semi-Markovian evolution of the density matrix's diagonal elements.
• The memory kernel alone can lead to evolutions that are not completely positive.
• The inclusion of the decoherence generator restores complete positivity to the overall quantum evolution.

Conclusions:

• A new class of quantum evolution beyond Markovian semigroup is established, incorporating memory effects via a hybrid generator.
• The interplay between memory-controlled dissipation and quantum decoherence is essential for maintaining complete positivity.
• This framework offers a more comprehensive description of open quantum systems, particularly for qubit dynamics.