This means that using the information of how state |1⟩ decoheres with other states |j⟩ / ∈ {|0⟩, |1⟩} allows us to determine how the random phase θ ξ should be partitioned among θ 0,ξ and θ 1,ξ . Eq. 64 suggests that there is no need to add additional random phase to coefficients c 1,ξ (t) if one wants to correctly describe the decoherence dynamics between state |1⟩ and |j⟩ (for j ̸ = 0, 1) governed by Lindblad dynamics (Eq. 24). The information in Eq. 63 was omitted when developing the Ehrenfest+R method. Nevertheless, the same choice was empirically discovered through the use of numerical simulations of Ehrenfest+R. Using a similar analysis of the above procedure for the left-hand side of Eq. 38b, together with Eq. 45 and Eq. 66, it follows that