Markovian semigroup from mixing non-invertible dynamical maps

Abstract

We analyze the convex combinations of non-invertible generalized Pauli dynamical maps. By manipulating the mixing parameters, one can produce a channel with shifted singularities, additional singularities, or even no singularities whatsoever. In particular, we show how to use non-invertible dynamical maps to produce the Markovian semigroup. Interestingly, the maps whose mixing results in a semigroup are generated by the time-local generators and time-homogeneous memory kernels that are not regular; i.e., their formulas contain infinities. Finally, we show how the generators and memory kernels change after mixing the corresponding dynamical maps.

References in corpus (5)

• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Finding the Kraus decomposition from a master equation and vice versa
• Simulation of indivisible qubit channels in collision models
• Pauli Diagonal Channels Constant on Axes
• Memory kernel approach to generalized Pauli channels: Markovian, semi-Markov, and beyond