Sub-Heisenberg estimation of non-random phase-shifts

TL;DR

This paper demonstrates that it is possible to estimate small, deterministic phase-shifts with precision surpassing the Heisenberg limit by using non-linear estimators and vacuum coherence, challenging traditional quantum limits.

Contribution

It introduces a method to achieve sub-Heisenberg precision in phase-shift estimation using non-linear estimators and vacuum coherence.

Findings

Uncertainty below Heisenberg bound for fixed photon number

Utilization of non-linearity in estimators improves precision

Vacuum coherence enhances phase-shift detection

Abstract

We provide evidence that the uncertainty in detection of small and deterministic phase-shift deviations from a working point can be lower than the Heisenberg bound, for fixed finite mean number of photons. We achieve that by exploiting non-linearity of estimators and coherence with the vacuum.