Non-Markovianity of geometrical qudit decoherence

TL;DR

This paper extends the geometrical approach to qubit decoherence for higher-dimensional qudits, linking Markovian master equations to Fokker-Planck equations for quantum probability distributions.

Contribution

It generalizes the geometrical framework of qubit decoherence to qudits, providing a new perspective on their dynamics in higher dimensions.

Findings

Markovian master equations are equivalent to Fokker-Planck equations for quantum distributions

Analyzed examples include generalizations of the Pauli channel

Extended geometrical representation to higher-dimensional systems

Abstract

In the following paper, we generalize the geometrical framework of qubit decoherence to higher dimensions. The quantum mixed state is represented by the probability distribution, which is the K\"ahler function on the projective Hilbert space. The Markovian master equation for density operators turns out to be equivalent to the Fokker-Planck equation for quantum probability distributions. Several examples are analyzed, featuring different generalizations of the Pauli channel.