Interpolating between positive, Schwarz, and completely positive evolution for d-level systems

TL;DR

This paper explores a geometric framework for quantum dynamical maps in d-level systems, revealing how they transition between positive, Schwarz, and completely positive evolutions, and analyzing their Markovian properties.

Contribution

It introduces a geometric analysis of the parameter space for quantum maps, clarifying the structure of positivity regions and their impact on quantum evolution behavior.

Findings

Dynamical trajectories cross different positivity regions, illustrating transitions between regimes.

Within the studied class, evolutions become eventually entanglement breaking.

The analysis emphasizes the significance of divisibility and non-Markovianity in quantum dynamics.

Abstract

We study a class of quantum dynamical maps for d-level systems that interpolate between positive, Schwarz, and completely positive evolutions. Our approach is based on a geometric analysis of the parameter space, which reveals the structure of regions corresponding to different positivity classes and their boundaries. We show that dynamical trajectories naturally move across these regions, providing a clear geometric interpretation of transitions between Markovian and non-Markovian regimes. It is shown that within presented class the evolution becomes eventually entanglement breaking. This analysis highlights the role of divisibility and eternally non-Markovian evolution.