Kramers-Kronig relations and precision limits in quantum phase estimation

TL;DR

This paper explores the fundamental limits of quantum phase estimation under loss, linking the precision bounds to Kramers-Kronig relations and showing how loss constrains achievable measurement accuracy.

Contribution

It introduces a physical interpretation of precision bounds in quantum metrology based on Kramers-Kronig relations, connecting phase and loss estimation limits.

Findings

Kramers-Kronig relations underpin the ultimate bounds in quantum phase estimation.

Loss imposes fundamental constraints preventing Heisenberg scaling.

Precision on phase estimation is intrinsically linked to loss measurement accuracy.

Abstract

The ultimate precision in any measurement is dictated by the physical process implementing the observation. The methods of quantum metrology have now succeeded in establishing bounds on the achievable precision for phase measurements over noisy channels. In particular, they demonstrate how the Heisenberg scaling of the precision can not be attained in these conditions. Here we discuss how the ultimate bound in presence of loss has a physical motivation in the Kramers-Kronig relations and we show how they link the precision on the phase estimation to that on the loss parameter.