Quantum filtering for multiple input multiple output systems driven by arbitrary zero-mean jointly Gaussian input fields

TL;DR

This paper develops a comprehensive quantum filtering framework for MIMO systems driven by arbitrary zero-mean jointly Gaussian fields, extending classical methods to quantum contexts and covering various Gaussian states.

Contribution

It derives the general quantum filtering equation for MIMO systems with any zero-mean Gaussian input fields, broadening the scope of quantum filtering theory.

Findings

Derivation of the quantum filtering equation for MIMO systems with Gaussian inputs

Applicable to vacuum, squeezed, thermal, and squeezed thermal states

Includes mild assumptions on certain matrix ranks

Abstract

In this paper, we treat the quantum filtering problem for multiple input multiple output (MIMO) Markovian open quantum systems coupled to multiple boson fields in an arbitrary zero-mean jointly Gaussian state, using the reference probability approach formulated by Bouten and van Handel as a quantum version of a well-known method of the same name from classical nonlinear filtering theory, and exploiting the generalized Araki-Woods representation of Gough. This includes Gaussian field states such as vacuum, squeezed vacuum, thermal, and squeezed thermal states as special cases. The contribution is a derivation of the general quantum filtering equation (or stochastic master equation as they are known in the quantum optics community) in the full MIMO setup for any zero-mean jointy Gaussian input field states, up to some mild rank assumptions on certain matrices relating to the measurement vector.