Back-Action-Evading Measurements and Quantum Non-Demolition Variables via Linear Systems Engineering

TL;DR

This paper develops a unified framework for implementing back-action-evading and quantum non-demolition measurements in linear quantum systems, enhancing precision in quantum metrology and sensing.

Contribution

It introduces a structural theory that identifies conditions for BAE and QND measurements using linear system engineering, including feedback control for non-compliant systems.

Findings

Key Hamiltonian condition enables BAE measurements of conjugate variables.

Symmetric coupling yields QND variables.

Coherent feedback can engineer BAE measurements in non-compliant systems.

Abstract

We establish a framework for realizing back-action-evading (BAE) measurements and quantum non-demolition (QND) variables in linear quantum systems. The key condition, a purely imaginary Hamiltonian with a real or imaginary coupling operator, enables BAE measurements of conjugate observables. Symmetric coupling further yields QND variables. For non-compliant systems, coherent feedback can engineer BAE measurements. Crucially, the QND interaction condition simultaneously ensures BAE measurements and promotes the coupling operator to a QND observable. This work provides a unified structural theory for enhancing precision in quantum metrology and sensing.