# Quantum enhanced estimation of diffusion

## TL;DR

This paper demonstrates that quantum squeezing significantly enhances the precision of estimating momentum diffusion in macroscopic quantum systems, with implications for testing collapse theories and improving optomechanical sensing.

## Contribution

It shows that quantum squeezing improves diffusion measurement accuracy, reducing experimental times and enabling tests of collapse models.

## Key findings

- 10dB of squeezing reduces required free-fall time by a factor of ten
- Momentum measurement outperforms other quadratures by a factor of three
- Implications for ruling out certain spontaneous collapse theories and enhancing sensing

## Abstract

Momentum diffusion is a possible mechanism for driving macroscopic quantum systems towards classical behaviour. Experimental tests of this hypothesis rely on a precise estimation of the strength of this diffusion. We show that quantum-mechanical squeezing offers significant improvements, including when measuring position. For instance, with 10dB of mechanical squeezing, experiments would require a tenth of proposed free-fall times. Momentum measurement is better by an additional factor of three, while another quadrature is close to optimal. These have particular implications for the space-based MAQRO proposal -- where it could rule out the spontaneous collapse theory due to Ghirardi, Rimini, and Weber -- as well as terrestrial optomechanical sensing.