  We investigate the validity of quantum regression for a family of quantum
Hamiltonians on a multipartite system leading to phase-damping reduced
dynamics. After finding necessary and sufficient conditions for the
CP-divisibility of the corresponding channel, we evaluate a hierarchy of
equations equivalent to the validity of quantum regression under arbitrary
interventions; in particular, we find necessary conditions for a nontrivial
dephasing to be compatible with quantum regression. In this framework, we study
a class of dephasing-type generalized spin-boson (GSB) models, investigating
the existence of qubit-environment coupling functions that ensure the exact
validity of quantum regression.
