# Dissipative generators, divisible dynamical maps and Kadison-Schwarz inequality

## TL;DR

This paper introduces Kadison-Schwarz divisible dynamical maps as a generalization of CP-divisibility, characterizing quantum Markovian evolution through time-local dissipative generators, with illustrative qubit examples.

## Contribution

It defines and characterizes Kadison-Schwarz divisible maps, extending the framework of quantum Markovian dynamics beyond CP-divisibility.

## Key findings

- Kadison-Schwarz divisible maps are characterized by time-local dissipative generators
- The concept generalizes CP-divisibility in quantum Markovian evolution
- Illustrative qubit evolution demonstrates the new concept

## Abstract

We introduce a concept of Kadison-Schwarz divisible dynamical maps. It turns out that it is a natural generalization of the well known CP-divisibility which characterizes quantum Markovian evolution. It is proved that Kadison-Schwarz divisible maps are fully characterized in terms of time-local dissipative generators. Simple qubit evolution illustrates the concept.