The Ehrenfest+R approach was derived under the condition that Γ ≪ E, where Γ is the decay rate of the jump operator L and E is the energy difference between state |0⟩ and |1⟩ (see Appendix A). This condition is thus the regime where the Ehrenfest+R approach can be applied with guaranteed accuracy. The L-MFE method, on the other hand, does not have any restrictions on the parameter regimes where it is applicable.