This paper investigates the validity of quantum regression for a specific class of quantum systems that induce phase-damping. The analysis reveals that nontrivial phase-damping and quantum regression are only compatible when parts of the total system-bath Hamiltonian don't commute. The study focuses on scenarios like the spin-boson model, exploring coupling functions where quantum regression holds exactly or approximately, especially under specific limits like "flat" coupling.

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This paper presents a robust theoretical analysis of quantum regression in dephasing phenomena. It offers valuable insights into the conditions required for quantum regression to hold and connects them to the dynamics of open quantum systems. The clear mathematical formulations and the exploration of different models strengthen the paper. While primarily theoretical and with specific model assumptions, the depth of the analysis and its contribution to understanding non-Markovian dynamics merit a strong rating. No obvious conflicts of interest were identified.