# Quantum sensing of curvature

## TL;DR

This paper explores quantum methods for measuring the curvature of surfaces by analyzing particles constrained to those surfaces, using quantum estimation theory to identify optimal measurement strategies.

## Contribution

It introduces a quantum estimation framework for curvature sensing on manifolds, providing explicit results for free particles and magnetic field scenarios.

## Key findings

- Position measurements nearly optimal for radius estimation
- Quantum estimation theory quantifies information encoding in particle states
- Explicit results for spheres and cylinders

## Abstract

We address the problem of sensing the curvature of a manifold by performing measurements on a particle constrained to the manifold itself. In particular, we consider situations where the dynamics of the particle is quantum mechanical and the manifold is a surface embedded in the three-dimensional Euclidean space. We exploit ideas and tools from quantum estimation theory to quantify the amount of information encoded into a state of the particle, and to seek for optimal probing schemes, able to actually extract this information. Explicit results are found for a free probing particle and in the presence of a magnetic field. We also address precision achievable by position measurement, and show that it provides a nearly optimal detection scheme, at least to estimate the radius of a sphere or a cylinder.