Filtering equation for a measurement of a coherent channel

TL;DR

This paper develops a stochastic filtering model for continuous photon counting and heterodyne measurement of a coherent quantum source, deriving nonlinear equations for the posterior state of a cavity field using quantum stochastic calculus.

Contribution

It introduces a new nonlinear filtering equation for a single-mode cavity field under continuous measurement, extending quantum filtering theory to coherent sources.

Findings

Derived nonlinear filtering equations for counting and diffusion measurements.

Provided posterior dynamics for a Bose field initially in a coherent state.

Enhanced understanding of quantum measurement processes for coherent channels.

Abstract

A stochastic model for a continuous photon counting and heterodyne measurement of a coherent source is proposed. A nonlinear filtering equation for the posterior state of a single-mode field in a cavity is derived by using the methods of quantum stochastic calculus. The posterior dynamics is found for the observation of a Bose field being initially in a coherent state. The filtering equations for counting and diffusion processes are given.