01444nas a2200169   4500000000100000000000100001008004100002260001200043100001800055700002300073700002200096700002200118245006400140856004600204490000700250520101700257       2022                            d  c08/20221 aKoorosh Sadri1 aFereshte Shahbeigi1 aZbigniew Puchała1 aKarol Życzkowski00aAccessible maps in a group of classical or quantum channels  uhttps://doi.org/10.1142/S12301612225000200 v293 a<p>We study the problem of accessibility in a set of classical and quantum channels admitting a group structure. Group properties of the set of channels, and the structure of the closure of the analyzed group <em>G</em> plays a pivotal role in this regard. The set of all convex combinations of the group elements contains a subset of channels that are accessible by a dynamical semigroup. We demonstrate that accessible channels are determined by probability vectors of weights of a convex combination of the group elements, which depend neither on the dimension of the space on which the channels act, nor on the specific representation of the group. Investigating geometric properties of the set <em>A</em> of accessible maps we show that this set is non-convex, but it enjoys the star-shape property with respect to the uniform mixture of all elements of the group. We demonstrate that the set <em>A</em> covers a positive volume in the polytope of all convex combinations of the elements of the group.</p>