Metrological advantage at finite temperature for Gaussian phase estimation

TL;DR

This paper defines a measure of metrological advantage in Gaussian phase estimation considering thermal noise, showing squeezing is necessary and sufficient for advantage in isotropic non-pure Gaussian states, advancing nonclassicality quantification.

Contribution

It introduces a new definition of metrological advantage accounting for thermal noise and proves squeezing is both necessary and sufficient for advantage in certain Gaussian states.

Findings

Squeezing is necessary and sufficient for metrological advantage in isotropic non-pure Gaussian states.

The work interprets results within resource theory of quantum states.

Discusses alternative sources of advantage beyond squeezing.

Abstract

In the context of phase estimation with Gaussian states, we introduce a quantifiable definition of metrological advantage that takes into account thermal noise in the preparation procedure. For a broad set of states, \textit{isotropic non-pure Gaussian states}, we show that squeezing is not only necessary, but sufficient, to achieve metrological advantage. We interpret our results in the framework of resource theory, and discuss possible sources of advantage other than squeezing. Our work is a step towards using phase estimation with pure and mixed state to define and quantify nonclassicality. This work is complementary with studies that defines nonclassicality using quadrature displacement estimation.