Entanglement Breaking Structure of Cartan-Covariant Quantum Channels

Cartan-covariant quantum channels are introduced and studied using the Choi-Jamio{\l}kowski isomorphism. The channels are Cartan-covariant as the covariance groups considered form symmetric pairs with the special unitary group SU($n$), and their associated Cartan involution provides a route to exactly compute the eigenspectrum of their Choi states and the partial transpose for any $n\in \mathbb{N}$. These channels include previously studied SO$(n)$-covariant channels, and further include Sp$(\frac{n}{2})$-covariant channels (when $n$ is even) and S(U($p$) $\times$ U($q$))-covariant channels (where $n\!=\!p\!+\!q$). We show that all Cartan-covariant channels satisfy the PPT$^{2}$-conjecture and further demonstrate the nontrivial nature of this result for the class of Sp$(\frac{n}{2})$-covariant and ${\rm S}({\rm U}(p) \!\times\!{\rm U}(q))$-covariant channels