Multiparameter Heisenberg limit

TL;DR

This paper derives a universal quantum Heisenberg limit for multiparameter estimation, demonstrating quadratic scaling of mean-square error with quantum resources, applicable to Gaussian priors and optical phase estimation.

Contribution

It introduces a quantum Bell-Ziv-Zakai bound to establish a fundamental limit on multiparameter estimation accuracy for Gaussian priors.

Findings

Mean-square error scales quadratically with quantum resources.

The bound applies universally to Gaussian prior distributions.

Results are relevant for optical phase estimation scenarios.

Abstract

Using a quantum version of the Bell-Ziv-Zakai bound, I derive a Heisenberg limit to multiparameter estimation for any Gaussian prior probability density. The mean-square error lower bound is shown to have a universal quadratic scaling with respect to a quantum resource, such as the average photon number in the case of optical phase estimation, suitably weighted by the prior covariance matrix.