  Quantum Markov models are employed ubiquitously in quantum physics and in
quantum information theory due to their relative simplicity and analytical
tractability. In particular, these models are known to give accurate
approximations for a wide range of quantum optical and mesoscopic systems.
However, in general, the validity of the Markov approximation entails
assumptions regarding properties of the system of interest and its environment,
which may not be satisfied or accurate in arbitrary physical systems.
Therefore, developing useful modelling tools for general non-Markovian quantum
systems for which the Markov approximation is inappropriate or deficient is an
undertaking of significant importance. This work considers non-Markovian
principal quantum systems that can be embedded in a larger Markovian quantum
system with one or more compound baths consisting of an auxiliary quantum
system and a quantum white noise field, and derives a set of coupled stochastic
and quantum master equations for embedded non-Markovian quantum systems. The
case of a purely Hamiltonian coupling between the principal and auxiliary
systems as a closed system without coupling to white noises is included as a
special case. The results are expected to be of interest for (open-loop and
feedback) control of continuous-time non-Markovian systems and studying reduced
models for numerical simulation of such systems. They may also shed more light
on the general structure of continuous-time non-Markovian quantum systems.
