Entanglement Breaking Structure of Cartan-Covariant Quantum Channels

Abstract

Cartan-covariant quantum channels are introduced and studied using the Choi-Jamiołkowski 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 $\mathrm{S}(\mathrm{U}(p)\times \mathrm{U}(q))$-covariant channels

21 pages, 2 figures