Quantum filter processes driven by Markovian white noises have classical versions

TL;DR

This paper demonstrates how certain quantum filters driven by Markovian white noises can be represented with classical versions by leveraging their quantum Markovian properties and classical filtering techniques.

Contribution

It introduces a method to construct classical versions of quantum filters driven by Wiener and Poisson noises using quantum Markovian components.

Findings

Classical versions of quantum filters are derived from quantum white noises.

The approach uses classical recursive filtering equations.

Applicable to filters driven by Wiener and Poisson processes.

Abstract

We study quantum filters that are driven by basic quantum noises and construct classical versions. Our approach is based on exploiting the quantum markovian component of the observation and measurement processes of the filters. This approach leads in a natural way the classical versions for a class of quantum filters. We consider quantum white noises derived from Wiener and Poisson processes that drive the signal and measurement processes and derive the recursive filtering equations using classical machinery.