Gaussian interferometric power

TL;DR

This paper extends the concept of interferometric power to continuous-variable Gaussian states in optical interferometry, providing a closed-form formula and analyzing the metrological advantages of different Gaussian states.

Contribution

It introduces a Gaussian version of interferometric power, deriving a closed formula for two-mode states and comparing the metrological performance of various Gaussian states.

Findings

Separable and entangled Gaussian states can maximize interferometric power.

Thermalized states can outperform pure squeezed states at fixed entanglement.

The study discusses the scaling of quantum Fisher information in this context.

Abstract

The interferometric power of a bipartite quantum state quantifies the precision, measured by quantum Fisher information, that such a state enables for the estimation of a parameter embedded in a unitary dynamics applied to one subsystem only, in the worst-case scenario where a full knowledge of the generator of the dynamics is not available a priori. For finite-dimensional systems, this quantity was proven to be a faithful measure of quantum correlations beyond entanglement. Here we extend the notion of interferometric power to the technologically relevant setting of optical interferometry with continuous-variable probes. By restricting to Gaussian local dynamics, we obtain a closed formula for the interferometric power of all two-mode Gaussian states. We identify separable and entangled Gaussian states which maximize the interferometric power at fixed mean photon number of the probes, and discuss the associated metrological scaling. At fixed entanglement of the probes, highly thermalized states can guarantee considerably larger precision than pure two-mode squeezed states.