Markovian semigroup from mixing non-invertible dynamical maps

TL;DR

This paper explores how mixing non-invertible dynamical maps can produce Markovian semigroups, revealing new ways to generate Markovian dynamics from non-invertible channels with irregular generators.

Contribution

It demonstrates how to obtain Markovian semigroups by mixing non-invertible generalized Pauli maps, even when generators contain infinities, expanding understanding of non-Markovian to Markovian transitions.

Findings

Mixing parameters can shift or remove singularities in dynamical maps.

Markovian semigroups can be generated from non-invertible maps with irregular generators.

The structure of generators and memory kernels changes under mixing.

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.