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

TL;DR

This paper introduces Cartan-covariant quantum channels, analyzes their positivity properties, and proves the PPT$^{2}$ conjecture for these channels across all dimensions, advancing understanding of quantum channel structure.

Contribution

It presents a new class of channels with a Lie group covariance structure and proves the PPT$^{2}$ conjecture for them in all dimensions.

Findings

Characterization of completely positive and co-positive regions

Spectral analysis of the Choi state

Proof of the PPT$^{2}$ conjecture for Cartan-covariant channels

Abstract

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.