For the two-level special case, it reduces to K(θ) = 1 2 sin θ. Our definition of K n (θ n ) in Eq. 22 is different than the one derived by Tilma and Nemoto. We find that this new expression of dΩ guarantees the identity relation of Eq. 20 and a correct distribution for each angle θ n . The proof of the current differential phase-space volume element definition is given in Appendix C. To simplify our notation, we define the expectation value of the generalized spin operator as