Cartan-covariant Quantum Channels and the PPT$^{2}$ conjecture

Two-parameter generalizations of depolarizing channels are introduced and studied. These so-called Cartan-covariant channels have a covariance Lie group that forms a Cartan decomposition of SU$(D)$. The regions of completely positive and completely co-positive Cartan-covariant trace-preserving maps are found through a spectral analysis of the Choi state. Furthermore, we prove that the PPT$^{2}$ conjecture holds for these channels in any dimension.