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Positivity preservation is naturally guaranteed in exact non-Markovian masterequations for open quantum system dynamics. However, in many approximatednon-Markovian master equations, the positivity of the reduced density matrix isnot guaranteed. In this paper, we provide a general class of time-local,perturbative and positivity-preserving non-Markovian master equations generatedfrom stochastic Schrodinger equations, particularly quantum-state-diffusionequations. Our method has an expanded range of applicability for accommodatinga variety of non-Markovian environments. We show the positivity-preservingmaster equation for a three-level system coupled to a dissipative bosonicenvironment as a particular example to exemplify our general approach. Weillustrate the numerical simulations with an analysis explaining why theprevious approximated non-Markovian master equations cannot guaranteepositivity. Our work provides a consistent master equation for studying thenon-Markovian dynamics in ultrafast quantum processes and strong-couplingsystems.

Positivity Preserving non-Markovian Master Equation for Open Quantum System Dynamics: Stochastic Schr\"{o}dinger Equation Approach