where ρ denotes the full density operator and ρs is the RDM operator for the system by tracing out the bath DOF. Note that the coherence in this definition is basis-dependent and can lead to qualitatively different results with a change of basis when analyzing decoherence dynamics. Purity, Tr s [ρ 2 s (t)] on the other hand, is representation-independent. Here, we investigate ρ +-(t) because it is closely connected with the 2DES spectra measured experimentally (off-diagonal beating signals which correspond to the cross peak of |+⟩ and |-⟩ states).