Kraus representation of quantum evolution and fidelity as manifestations of Markovian and non-Markovian avataras

TL;DR

This paper demonstrates that fidelity measures can distinguish between Markovian and non-Markovian quantum dynamics, using Kraus representation to analyze short-time behavior and illustrating with four interaction models.

Contribution

It introduces a fidelity-based signature for non-Markovianity derived from Kraus representation and compares Markovian and non-Markovian features through concrete models.

Findings

Fidelity with initial state is higher in non-Markovian evolution.

Fidelity with earlier states signals non-Markovian dynamics.

Kraus representation reveals short-time distinctions between dynamics.

Abstract

It is shown that the fidelity of the dynamically evolved system with its earlier time density matrix provides a signature of non-Markovian dynamics. Also, the fidelity associated with the initial state and the dynamically evolved state is shown to be larger in the non-Markovian evolution compared to that in the corresponding Markovian case. Starting from the Kraus representation of quantum evolution, the Markovian and non-Markovian features are discerned in its short time structure. These two features are in concordance with each other and they are illustrated with the help of four models of interaction of the system with its environment.