Toward Incompatible Quantum Limits on Multiparameter Estimation

TL;DR

This paper proposes a new criterion for multiparameter quantum estimation that can surpass traditional limits by increasing parameter variances, demonstrated with high-precision optical measurements using Hermite-Gaussian states.

Contribution

It introduces a novel criterion to mitigate incompatibility in quantum multiparameter estimation and demonstrates its effectiveness with experimental high-precision optical measurements.

Findings

Achieved simultaneous precisions of 1.45 nm and 4.08 nrad in experiment.

Proposed a scheme using high-order Hermite-Gaussian states as probes.

Provided deeper insight into the Heisenberg uncertainty's role in quantum metrology.

Abstract

Achieving the ultimate precisions for multiple parameters simultaneously is an outstanding challenge in quantum physics, because the optimal measurements for incompatible parameters cannot be performed jointly due to the Heisenberg uncertainty principle. In this work, a criterion proposed for multiparameter estimation provides a possible way to beat this curse. According to this criterion, it is possible to mitigate the influence of incompatibility meanwhile improve the ultimate precisions by increasing the variances of the parameter generators simultaneously. For demonstration, a scheme involving high-order Hermite-Gaussian states as probes is proposed for estimating the spatial displacement and angular tilt of light at the same time, and precisions up to 1.45 nm and 4.08 nrad are achieved in experiment simultaneously. Consequently, our findings provide a deeper insight into the role of Heisenberg uncertainty principle in multiparameter estimation, and contribute in several ways to the applications of quantum metrology.