Quantum Trajectories for Squeezed Input Processes: Explicit Solutions

TL;DR

This paper derives explicit solutions for quantum filtering equations involving Gaussian input states, enabling better understanding of quantum trajectories under continuous measurement for Gaussian states.

Contribution

It provides explicit solutions to quantum filtering equations for systems driven by Gaussian states, extending previous work to non-zero mean inputs using characteristic functions.

Findings

Explicit solutions for quantum filtering with Gaussian inputs.

Applicable to systems with non-zero mean Gaussian states.

Enhances understanding of quantum trajectories under continuous measurement.

Abstract

We consider the quantum (trajectories) filtering equation for the case when the system is driven by Bose field inputs prepared in an arbitrary non-zero mean Gaussian state. The a posteriori evolution of the system is conditioned by the results of a single or double homodyne measurements. The system interacting with the Bose field is a single cavity mode taken initially in a Gaussian state. We show explicit solutions using the method of characteristic functions to the filtering equations exploiting the linear Gaussian nature of the problem.