Complete positivity, finite-temperature effects, and additivity of noise for time-local qubit dynamics

We present a general model of qubit dynamics which entails pure dephasing and dissipative time-local master equations. This allows us to describe the combined effect of thermalization and dephasing beyond the usual Markovian approximation. We investigate the complete positivity conditions and introduce a heuristic model that is always physical and provides the correct Markovian limit. We study the effects of temperature on the non-Markovian behavior of the system and show that the noise additivity property discussed by Yu and Eberly [Phys. Rev. Lett. 97, 140403 (2006)] holds beyond the Markovian limit.