Memory kernel approach to generalized Pauli channels: Markovian, semi-Markov, and beyond

Abstract

In this paper, we analyze the evolution of the generalized Pauli channels governed by the memory kernel master equation. We provide necessary and sufficient conditions for the memory kernel to give rise to the legitimate (completely positive and trace-preserving) quantum evolution. In particular, we analyze a class of kernels generating the quantum semi-Markov evolution, which is a natural generalization of the Markovian semigroup. Interestingly, the convex combination of Markovian semigroups goes beyond the semi-Markov case. Our analysis is illustrated with several examples.

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Cited by in corpus (19)

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• Irreversible quantum evolution with quadratic generator: Review
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• Quantum channels irreducibly covariant with respect to the finite group generated by the Weyl operators
• Classical capacity of the generalized Pauli channels
• Maximally non-Markovian quantum dynamics without environment backflow of information
• How quantum evolution with memory is generated in a time-local way
• Stochastic collision model approach to transport phenomena in quantum networks
• Quantum non-Markovian environment-to-system backflows of information: non-operational vs. operational approaches
• Markovian semigroup from mixing non-invertible dynamical maps
• Engineering fidelity of the generalized Pauli channels via legitimate memory kernels
• Detection of Bidirectional System-Environment Information Exchanges
• A solvable class of non-Markovian quantum multipartite dynamics
• Regularized maximal fidelity of the generalized Pauli channels
• Engineering classical capacity of generalized Pauli channels with admissible memory kernels
• Improving classical capacity of qubit dynamical maps through stationary state manipulation
• Accessible maps in a group of classical or quantum channels