Enhancement of the metrological sensitivity limit through knowledge of the average energy

TL;DR

This paper demonstrates that quantum phase estimation sensitivity can be improved beyond the classical bound by utilizing prior knowledge of the energy expectation, leading to significant gains in atomic clock precision.

Contribution

It introduces a method to surpass the classical Cramér-Rao bound in quantum phase estimation using energy expectation knowledge, with practical implications for atomic clocks.

Findings

Sensitivity exceeds classical Cramér-Rao bound with energy knowledge

Linear scaling of sensitivity gain with number of atoms

Small observable modifications significantly impact sensitivity

Abstract

We consider the problem of quantum phase estimation with access to arbitrary measurements in a single suboptimal basis. The achievable sensitivity limit in this case is determined by the classical Cram\'{e}r-Rao bound with respect to the fixed basis. Here we show that the sensitivity can be enhanced beyond this limit if knowledge about the energy expectation value is available. The combined information is shown to be equivalent to a direct measurement of an optimal linear combination of the basis projectors and the phase-imprinting Hamiltonian. Application to an atomic clock with oversqueezed spin states yields a sensitivity gain that scales linearly with the number of atoms. Our analysis further reveals that small modifications of the observable can have a strong impact on the sensitivity.