Interferometric Phase Estimation Though Quantum Filtering in Coherent States

TL;DR

This paper develops a quantum filtering approach for interferometric phase estimation using continuous non-demolition measurements on coherent states, applicable to quadrature homodyne and photon-counting detection schemes.

Contribution

It derives a general quantum filter equation for phase estimation in interferometers with coherent input fields, covering multiple detection methods and providing solutions for specific cases.

Findings

Derived the quantum filter equation for coherent state inputs.

Unified treatment of homodyne and photon-counting detection schemes.

Provided solutions for a specific linearized filter application.

Abstract

We derive the form of the quantum filter equation describing the continuous observation of the phase of a quantum system in an arm of an interferometer via non-demolition measurements when the statistics of an input field used for the indirect measurement are in a general coherent state. Both quadrature homodyne detection and photon-counting dection schemes are covered, and we solve the linearized filter for a specific application.