Divisibility of quantum dynamical maps and collision models

TL;DR

This paper explores the divisibility properties of quantum dynamical maps using collision models, introducing ultimate CP divisible processes and analyzing their stability and non-Markovian behavior.

Contribution

It introduces the concept of ultimate CP divisible processes, characterizes Pauli semigroups with this property, and constructs collision models for various types of quantum evolutions.

Findings

Ultimate CP divisible processes lose divisibility under perturbations.

Collision models can realize additive and multiplicative generator properties.

Mixtures of dynamical maps can produce eternal CP indivisible evolutions.

Abstract

Divisibility of dynamical maps is visualized by trajectories in the parameter space and analyzed within the framework of collision models. We introduce ultimate completely positive (CP) divisible processes, which lose CP divisibility under infinitesimal perturbations, and characterize Pauli dynamical semigroups exhibiting such a property. We construct collision models with factorized environment particles, which realize additivity and multiplicativity of generators of CP divisible maps. A mixture of dynamical maps is obtained with the help of correlated environment. Mixture of ultimate CP divisible processes is shown to result in a new class of eternal CP indivisible evolutions. We explicitly find collision models leading to weakly and essentially non-Markovian Pauli dynamical maps.