Accessible Maps in a Group of Classical or Quantum Channels

The question

Start with a group of classical or quantum channels and form mixtures of its elements. Which of these mixtures can be generated by continuous-time dynamical semigroups?

The work

The paper characterizes accessible channels through the probability weights of their mixtures. These weights are independent of the dimension of the underlying space and of the particular representation of the group.

The accessible set has a distinctive geometry: it need not be convex, but it is star-shaped around the uniform mixture of the group elements and occupies a positive volume within the surrounding polytope. This connects the structure of a channel group to the dynamics it can generate.