Source-linked AI summary
Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
Heinz-Peter Breuer, Elsi-Mari Laine, Jyrki Piilo
TL;DR
The paper addresses how to define and quantify quantum non-Markovianity without relying on a specific dynamical representation. It constructs a trace-distance-based measure whose nonzero value signals information backflow from the environment to the system.
Problem
The paper asks how to rigorously define and quantify quantum non-Markovianity independently of any specific representation or master-equation approximation.
Method
The measure N(Φ) is constructed as a functional of the dynamical map using the trace distance between two evolving quantum states and maximizing over initial-state pairs.
Results
A process is non-Markovian when the trace distance increases for some state pair and time, indicating information flow from the environment back to the system.
Takeaways & Limitations
Observed trace-distance growth provides a clear signature and lower bound for non-Markovianity, supporting experimental validation without prior knowledge of the environment or interaction structure.
Abstract
from arXiv · showhide
We construct a general measure for the degree of non-Markovian behavior in open quantum systems. This measure is based on the trace distance which quantifies the distinguishability of quantum states. It represents a functional of the dynamical map describing the time evolution of physical states, and can be interpreted in terms of the information flow between the open system and its environment. The measure takes on nonzero values whenever there is a flow of information from the environment back to the open system, which is the key feature of non-Markovian dynamics.