Towards the Fundamental Quantum Limit of Linear Measurements of Classical Signals

TL;DR

This paper derives a fundamental quantum limit for classical signal measurements using linear detectors, connecting the quantum Cramér-Rao bound with the Standard Quantum Limit, and proposes new ways to enhance sensor sensitivity.

Contribution

It establishes a general condition for achieving the quantum limit in linear measurements and links it to quantum non-demolition measurement principles.

Findings

QCRB can be achieved with quantum non-demolition techniques

Test mass can be used as a resource to improve sensitivity

Application to gravitational wave detectors demonstrates practical relevance

Abstract

The quantum Cram\'er-Rao bound (QCRB) sets a fundamental limit for the measurement of classical signals with detectors operating in the quantum regime. Using linear-response theory and the Heisenberg uncertainty relation, we derive a general condition for achieving such a fundamental limit. When applied to classical displacement measurements with a test mass, this condition leads to an explicit connection between the QCRB and the Standard Quantum Limit which arises from a tradeoff between the measurement imprecision and quantum backaction; the QCRB can be viewed as an outcome of a quantum non-demolition measurement with the backaction evaded. Additionally, we show that the test mass is more a resource for improving measurement sensitivity than a victim of the quantum backaction, which suggests a new approach to enhancing the sensitivity of a broad class of sensors. We illustrate these points with laser interferometric gravitational wave detectors.