Quantum filter for a class of non-Markovian quantum systems

TL;DR

This paper introduces a Markovian framework to derive quantum filters for non-Markovian systems affected by Lorentzian noise, using an ancillary system to convert white noise into Lorentzian noise.

Contribution

It presents a novel approach to handle non-Markovian quantum systems by embedding them into an augmented Markovian system with an ancillary component.

Findings

Successfully derived quantum filters for non-Markovian systems

Demonstrated the approach with a practical example

Provided insights into non-Markovian dynamics and filtering

Abstract

In this paper we present a Markovian representation approach to constructing quantum filters for a class of non-Markovian quantum systems disturbed by Lorenztian 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. An example is provided to illustrate the non-Markovian dynamics of the principal system.