Quantum limit in continuous quantum measurement

TL;DR

This paper establishes a rigorous quantum noise inequality in continuous measurement, demonstrating that the minimum added noise equals zero-point noise, thus generalizing the Haus-Caves quantum limit beyond linear amplifiers.

Contribution

It introduces an explicit functional relation between quantum noise and the reduction operator, providing a new proof that the quantum limit equals zero-point noise, extending previous linear-response results.

Findings

Minimum noise added by the detector equals zero-point noise

Generalization of the Haus-Caves quantum limit for all quantum measurements

Analysis of back-action force statistics in reaching the quantum limit

Abstract

An inequality about quantum noise is presented with the imprecise measurement theory, which is used to analyse the quantum limit in continuous quantum measurement. Different from the linear-response approach based on the quantum relation between noise and susceptibilities of the detector, we provide an explicit functional relation between quantum noise and reduction operator, and show a rigorous result: The minimum noise added by the detector in quantum measurement is precisely equal to the zero-point noise. This conclusion generalizes the standard Haus-Caves quantum limit for a linear amplifier. We also discuss the statistic characters of the back-action force in quantum measurement and show on how to reach the quantum limit.