  Positivity preservation is naturally guaranteed in exact non-Markovian master
equations for open quantum system dynamics. However, in many approximated
non-Markovian master equations, the positivity of the reduced density matrix is
not guaranteed. In this paper, we provide a general class of time-local,
perturbative and positivity-preserving non-Markovian master equations generated
from stochastic Schrodinger equations, particularly quantum-state-diffusion
equations. Our method has an expanded range of applicability for accommodating
a variety of non-Markovian environments. We show the positivity-preserving
master equation for a three-level system coupled to a dissipative bosonic
environment as a particular example to exemplify our general approach. We
illustrate the numerical simulations with an analysis explaining why the
previous approximated non-Markovian master equations cannot guarantee
positivity. Our work provides a consistent master equation for studying the
non-Markovian dynamics in ultrafast quantum processes and strong-coupling
systems.
