Non-Markovianity of geometrical qudit decoherence

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.