# Do the eigenvalues of the Choi matrix have any direct physical interpretation?

Let $$\Phi\in\mathrm T(\mathcal X,\mathcal Y)$$ be a CPTP map, and let $$J(\Phi)$$ be its Choi representation. As is well known, any such map can be written in a Kraus representation of the form $$\Phi(X)=\sum_a p_a A_a X A_a^\dagger,\tag A$$ where $$p_a\ge0$$ and $$\operatorname{Tr}(A_a^\dagger A_b)=\delta_{ab}$$ (as mentioned for example in this other question of mine). The positive numbers $$p_a$$ appearing here can be seen to be the eigenvalues of $$J(\Phi)$$.

Is there a way to directly relate the eigenvalues $$p_a$$ to some properties of the channel, or to how the channel acts on states?