In this paper, we consider the convex set of d dimensional unital quantum
channels. In particular, we parametrise a family of maps and through this
parametrisation we provide a partial characterisation of the set of unital
quantum maps with respect to this family of channels. For the case of qutrit
channels, we consider the extreme points of the set and their classification
with respect to the Kraus rank. In this setting, we see that the parametrised
family of maps corresponds to maps with Kraus rank three. Furthermore, we
introduce a novel family of qutrit unital quantum channels with Kraus rank four
to consider the extreme points of the set over all possible Kraus ranks. We
construct explicit examples of these two families of channels and we consider
the question of whether these channels correspond to extreme points of the set
of quantum unital channels. Finally, we demonstrate how well-known channels
relate to the examples presented.Comment: 18 page