). This model contains the third state |2⟩, which is coupled to state |0⟩. Note that in the L-MFE algorithm, when the jump operator is L = |0⟩⟨1|, state |0⟩ is the state that gains random phases (see Eq. 65). Thus, the preservation of correct dynamics when random phases interact with states {|j⟩} outside of the reduced density matrix of |0⟩ and |1⟩ is tested. In Fig. , the excited state shows exponential decay, while states |0⟩ and |2⟩ oscillate together until they reach a longtime population of 0.5, which is predicted by Lindblad dynamics. In Fig. , the corresponding imaginary parts of coherences Im[ρ 10 ] (orange), Im[ρ 12 ] (green), and Im[ρ 20 ] (red) are presented, and all of these coherences obtained from L-MFE (dotted) match the Lindblad dynamics (solid lines).