  We present a detailed derivation of the master equation describing a general
time-dependent quantum system with classical Poisson white noise and outline
its various properties. We discuss the limiting cases of Poisson white noise
and provide approximations for the different noise strength regimes. We show
that using the eigenstates of the noise superoperator as a basis can be a
useful way of expressing the master equation. Using this we simulate various
settings to illustrate different effects of Poisson noise. In particular, we
show a dip in the fidelity as a function of noise strength where high fidelity
can occur in the strong noise regime for some cases. We also investigate recent
claims [Jing et al., Phys. Rev. A 89 032110 (2014)] that this type of noise may
improve rather than destroy adiabaticity.
