Quantum filter for a class of non-Markovian quantum systems

In this paper we present a Markovian representation approach to constructing quantum filters for a class of non-Markovian quantum systems disturbed by Lorentzian noise. An ancillary system is introduced to convert white noise into Lorentzian noise which is injected into a principal system via a direct interaction. The resulting dynamics of the principal system are non-Markovian, which are driven by the Lorentzian noise. By probing the principal system, a quantum filter for the augmented system can be derived from standard theory, where the conditional state of the principal system can be obtained by tracing out the ancillary system.