# Measure for the Non-Markovianity of Quantum Processes

**Authors:** Heinz-Peter Breuer, Elsi-Mari Laine, Jyrki Piilo  
**arXiv:** [0908.0238](https://arxiv.org/abs/0908.0238)  
**Date:** 2009-08-03  
**Summary page:** https://www.summarizepaper.com/en/paper/0908.0238v1/

## Key points

- Heinz-Peter Breuer, Elsi-Mari Laine, and Jyrki Piilo propose a measure to quantify non-Markovian behavior in open quantum systems.
- The measure is based on the trace distance, which determines distinguishability between quantum states.
- The measure represents a functional of the dynamical map describing time evolution in these systems.
- It captures instances where information flows from the environment back to the open system.
- Researchers can use this measure to assess and analyze non-Markovian behavior in quantum processes.
- The measure provides a framework for studying information propagation over time in these systems.
- This research has implications for quantum information processing and communication.
- Accurately characterizing and controlling non-Markovian behavior is crucial for desired outcomes.
- The proposed measure contributes to understanding non-Markovian dynamics in open quantum systems.

## Summary

In their paper titled "Measure for the Non-Markovianity of Quantum Processes," Heinz-Peter Breuer, Elsi-Mari Laine, and Jyrki Piilo propose a comprehensive measure to quantify the degree of non-Markovian behavior in open quantum systems. The measure is based on the trace distance, which serves as a metric for determining the distinguishability between quantum states. The authors emphasize that their measure represents a functional of the dynamical map that describes the time evolution of physical states in these systems. It provides valuable insights into the information flow between the open system and its environment, capturing instances where there is a transfer of information from the environment back to the open system - considered a crucial characteristic of non-Markovian dynamics. By utilizing this measure, researchers can effectively assess and analyze non-Markovian behavior in various quantum processes. The proposed measure offers a quantitative framework to study and understand how information propagates within these systems over time. This work has significant implications for fields such as quantum information processing and quantum communication, where accurately characterizing and controlling non-Markovian behavior is essential for achieving desired outcomes. Overall, this research contributes to advancing our understanding of non-Markovian dynamics in open quantum systems by providing an innovative and reliable measure based on trace distance.