The Landau-Streater Channel as a Noisy Channel Model

In three dimensions, the Landau-Streater channel is nothing but the Werner-Holevo channel. Such a channel has no continuous parameter and hence cannot model an environmental noise. We consider its convex combination with the identity channel, making it suitable as a one-parameter noise model on qutrits. Moreover, whereas the original Werner-Holevo channel exhibits covariance under the complete unitary group $SU(3)$, the extended family maintains covariance only under the group $SO(3)$. This symmetry reduction allows us to investigate its impact on various properties of the original channel. Specifically, we examine its influence on the channel's spectrum, divisibility, complementary channel, and exact or approximate degradability, as well as its various kinds of capacities. Specifically, we derive analytical expressions for the one-shot classical capacity and the entanglement-assisted capacity, accompanied by the establishment of lower and upper bounds for the quantum capacity.